﻿<?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>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Related Party Transactions</ReportName>
  <ReportLongName>12001 - Disclosure - Related Party Transactions</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="Sep. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>Unit12</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Unit13</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Unit1</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Notes to Financial Statements</Label>
      <Level>0</Level>
      <ElementName>har_NotesToFinancialStatementsAbstract</ElementName>
      <ElementPrefix>har</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>Notes to Financial Statements [Abstract]</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 />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>Notes to Financial Statements [Abstract]</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Related Party Transactions</Label>
      <Level>1</Level>
      <ElementName>us-gaap_RelatedPartyTransactionsDisclosureTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <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>terselabel</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;div&gt;
&lt;p style="margin-top: 18px; margin-bottom: 0px;"&gt;&lt;font style="font-family: Times New Roman;" class="_mt" size="2"&gt;&lt;b&gt;Note 20 &amp;ndash; Related Party Transactions &lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="margin-top: 6px; margin-bottom: 0px;"&gt;&lt;font style="font-family: Times New Roman;" class="_mt" size="2"&gt;From time to time we enter into transactions with related parties. In December 2009, we entered into a three-year agreement for engineering and software development services with Neusoft Corporation ("Neusoft"), a Shanghai exchange listed technology solutions provider. A member of our Board of Directors is the Chairman and Chief Executive Officer of Neusoft. &lt;/font&gt;&lt;/p&gt;
&lt;p style="margin-top: 12px; margin-bottom: 0px;"&gt;&lt;font style="font-family: Times New Roman;" class="_mt" size="2"&gt;On April&amp;nbsp;20, 2010, our subsidiary, Innovative entered into an asset purchase and business transfer agreement (the "Asset Purchase Agreement") with Neusoft Technology Solutions GmbH ("Neusoft Technology"), which is a subsidiary of Neusoft for the sale of certain tangible assets located at Innovative's facility in Hamburg, Germany. This transaction closed on June&amp;nbsp;1, 2010. As part of the Asset Purchase Agreement, Innovative and Neusoft Technology entered into a five-year agreement for engineering and software development services related to Innovative's vehicle navigation business (the "Services Agreement"). Under the terms of the Asset Purchase Agreement, Innovative transferred at closing certain tangible assets and employment relationships to Neusoft Technology and received consideration of &amp;euro;6&amp;nbsp;million. Our subsidiary, Harman Becker and Neusoft Europe AG, a subsidiary of Neusoft, are guarantors under the terms of the Asset Purchase Agreement and the Services Agreement. During the three months ended September 30, 2010, we incurred total expenses of $5.6 million for engineering and software development services with Neusoft Technology and Neusoft. &lt;/font&gt;&lt;/p&gt;
&lt;p style="margin-top: 12px; margin-bottom: 0px; font-size: 1px;"&gt;&amp;nbsp;&lt;/p&gt; &lt;/div&gt;</NonNumbericText>
          <NonNumericTextHeader>Note 20 &amp;ndash; Related Party Transactions
From time to time we enter into transactions with related parties. In December 2009, we entered into a three-year</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>This element may be used for the entire related party transactions disclosure as a single block of text. Disclosure may include:  the nature of the relationship(s), a description of the transactions, the amount of the transactions, the effects of any change in the method of establishing the terms of the transaction from the previous period, stated interest rate, expiration date, terms and manner of settlement per the agreement with the related party, and amounts due to or from related parties. If the entity and one or more other entities are under common ownership or management control and this control affects the operating results or financial position, disclosure includes the nature of the control relationship even if there are no transactions between the entities. Disclosure may also include the aggregate amount of current and deferred tax expense for each statement of earnings presented where the entity is a member of a group that files a consolidated tax return, the amount of any tax related balances due to or from affiliates as of the date of each statement of financial position presented, the principal provisions of the method by which the consolidated amount of current and deferred tax expense is allocated to the members of the group and the nature and effect of any changes in that method. Examples of related party transactions include transactions between (a) a parent company and its subsidiary; (b) subsidiaries of a common parent; (c) and entity and its principal owners; and (d) affiliates.</ElementDefenition>
      <ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 04
 -Paragraph b
 -Article 3A

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 08
 -Paragraph k
 -Article 4

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher FASB
 -Name Statement of Financial Accounting Standard (FAS)
 -Number 57
 -Paragraph 1-4

</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <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>
