<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>11120 - Disclosure - Related Party Transactions</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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&lt;p style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&lt;b&gt;12. Related Party Transactions&lt;/b&gt;&lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;The Company rents its corporate office space from related parties affiliated through common ownership or management. The Company made payments for office rent, leasehold improvements and miscellaneous expenses aggregating $3.9&amp;#160;million during the year ended December&amp;#160;31, 2010 and $4.0&amp;#160;million during both the years ended December&amp;#160;31, 2011 and 2012 to the affiliated companies.&lt;/font&gt;&lt;/p&gt;
&lt;p style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;As of December&amp;#160;31, 2012, future rental commitments under outstanding agreements with the affiliated companies are approximately as follows (in thousands):&lt;/font&gt;&lt;/p&gt;
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&lt;!-- User-specified TAGGED TABLE --&gt;
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&lt;tr style="padding:0;"&gt;&lt;!-- TABLE COLUMN WIDTHS SET --&gt;
&lt;td style="FONT-FAMILY: times;" align="left"&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" width="12"&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" width="7" align="right"&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" width="45"&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" width="12"&gt;&lt;/td&gt;&lt;!-- TABLE COLUMN WIDTHS END --&gt;&lt;/tr&gt;
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&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;2013&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;3,481&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;" valign="bottom" bgcolor="white"&gt;
&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;2014&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;3,433&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;2015&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;3,177&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;" valign="bottom" bgcolor="white"&gt;
&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;2016&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;3,300&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;" valign="bottom" bgcolor="#CCEEFF"&gt;
&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;2017&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;3,429&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;" valign="bottom" bgcolor="white"&gt;
&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&lt;font size="2"&gt;Thereafter&lt;/font&gt;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;19,616&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0; FONT-SIZE: 1.5pt;" valign="top"&gt;
&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 1pt solid; FONT-FAMILY: times;" valign="bottom" colspan="2" align="right"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;" valign="bottom" bgcolor="#CCEEFF"&gt;
&lt;td style="FONT-FAMILY: times;"&gt;
&lt;p style="TEXT-INDENT: -10pt; FONT-FAMILY: times; MARGIN-LEFT: 10pt;"&gt;&amp;#160;&lt;/p&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;$&lt;/font&gt;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" align="right"&gt;&lt;font size="2"&gt;36,436&lt;/font&gt;&lt;/td&gt;
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&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="BORDER-BOTTOM: #000000 2.25pt double; FONT-FAMILY: times;" valign="bottom" colspan="2" align="right"&gt;&amp;#160;&lt;/td&gt;
&lt;td style="FONT-FAMILY: times;" valign="bottom"&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&gt;
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&lt;p style="FONT-FAMILY: times;"&gt;&lt;font size="2"&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;The Company provides contracted services, principally employee leasing services, to related parties affiliated through its equity investments in the BIR and Rehabilitation Institute of Denton,&amp;#160;LLC ("Denton") joint ventures. The provision of contracted services to BIR and Denton resulted in net operating revenues amounting to $92.2&amp;#160;million and $8.1&amp;#160;million, respectively for the year ended December&amp;#160;31, 2012; $53.3&amp;#160;million and $7.3&amp;#160;million, respectively for the year ended December&amp;#160;31, 2011 and $137&amp;#160;thousand for Denton for the year ended December&amp;#160;31, 2010.&lt;/font&gt;&lt;/p&gt;
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