<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.0.0.10</Version>
  <hasSegments>false</hasSegments>
  <ReportName>The Company and Basis of Presentation</ReportName>
  <ReportLongName>00100 - Disclosure - The Company and Basis of Presentation</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="3 Months Ended" />
        <Label Id="2" Label="Mar. 31, 2010" />
      </Labels>
      <CurrencyCode>usd</CurrencyCode>
      <CurrencySymbol>$</CurrencySymbol>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Note to Consolidated Financial Statements</Label>
      <Level>0</Level>
      <ElementName>fms_NotesToConsolidatedFinancialStatements</ElementName>
      <ElementPrefix>fms</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>The Company and Basis of Presentation</Label>
      <Level>1</Level>
      <ElementName>us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;1. &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;"&gt;   &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;"&gt;The Company and Basis of Presentation&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;The Company&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;Fresenius Medical Care AG &amp;amp; Co. KGaA ("FMC-AG &amp;amp; Co. KGaA"or the "Company") a German partnership limited by shares (Kommanditgesellschaft auf Aktien), is the world's largest kidney dialysis company, operating in both the field of dialysis services and the field of dialysis products for the treatment of end-stage renal disease ("ESRD"). The Company's dialysis business is vertically integrated, providing dialysis treatment at dialysis clinics it owns or operates and supplying these clinics with a broad range of products. In addition, the Company sells dialysis products to other dialysis service providers. In the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;United States&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, the Company also performs clinical laboratory testing and provides inpatient dialysis services and other services under contract to hospitals. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;In this Report, "FMC-AG &amp;amp; Co. KGaA," or the "Company," "we," "us" or "our" refers to the Company or the Company and its subsidiaries on a consolidated basis, as the context requires.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;Basis of Presentation&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;The accompanying consolidated financial statements have been prepared in accordance with &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;accounting principles generally accepted in the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;United States of America&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; ("&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;U.S. GAAP&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;")&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;The consolidated financial statements at March 31, 2010 and for the three-month periods ended March 31, 2010 and 2009 contained in this report are unaudited and should be read in conjunction with the consolidated financial statements contained in the Company's 2009 Annual Report on Form&amp;#160;20-F. &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;The preparation of consolidated financial statements &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;requires &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the consolidated financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;Such financial statements reflect all adjustments that, in the opinion of management, are necessary for a fair presentation of the results of the periods presented. All such adjustments are of a normal recurring nature.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;The results of operations for the three-month period ended March 31, 2010 are not necessarily indicative of the results of operations for the year ending December&amp;#160;31, 2010.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:6pt; margin-bottom:0pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:17px;"&gt;Income tax expense in the amount &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;of &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;$5&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;,004&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; for the three-month &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;period ending March 31&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;,&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; 2009&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; in the prior year's comparative consolidated financial statements has been reclassified to income attributable to noncontrolling interest to conform with the current year's presentation. &lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:0pt'&gt;&amp;#160;&lt;/p&gt;</NonNumbericText>
          <NonNumericTextHeader>1.    The Company and Basis of PresentationThe CompanyFresenius Medical Care AG &amp;amp; Co. KGaA ("FMC-AG &amp;amp; Co. KGaA"or the "Company") a German partnership</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDefenition>Description containing the entire organization, consolidation and basis of presentation of financial statements disclosure. May be provided in more than one note to the financial statements, as long as users are provided with an understanding of (1) the significant judgments and assumptions made by an enterprise in determining whether it must consolidate a VIE and/or disclose information about its involvement with a VIE, (2) the nature of restrictions on a consolidated VIE's assets reported by an enterprise in its statement of financial position, including the carrying amounts of such assets, (3) the nature of, and changes in, the risks associated with an enterprise's involvement with the VIE, and (4) how an enterprise's involvement with the VIE affects the enterprise's financial position, financial performance, and cash flows.  Describes procedure if disclosures are provided in more than one note to the financial statements.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name FASB Staff Position (FSP)
 -Number FAS140-4 and FIN46(R)-8
 -Paragraph 8, C1, C7

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Accounting Research Bulletin (ARB)
 -Number 51
 -Paragraph 2-6

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher AICPA
 -Name Statement of Position (SOP)
 -Number 94-6
 -Paragraph 10

Reference 4: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name FASB Interpretation (FIN)
 -Number 46R
 -Paragraph 4, 14, 15

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <ComparabilityReport>false</ComparabilityReport>
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
