We propose a model of Private Equity (PE) investment that can rationalize several empirical findings about fundraising and returns. General partners (GPs) possess superior investment skills and raise capital from Limited Partners (LPs) to finance illiquid projects within funds. The optimal fund contract incentivizes GPs to maximize the expected payoff of fund investments by giving them a profit share in the fund, while compensating LPs for the liquidity risk they face. The size of a PE fund increases with the amount of wealth the GP co-invests in the fund. When PE investments become attractive, GPs prefer to increase the size of their fund rather than increasing their profit share. In markets with low liquidity risk for LPs, expected returns to LPs are lower, and aggregate fundraising as well as average fund sizes are larger. When LPs can trade PE fund investments in a secondary market, partnership claims trade at a discount when aggregate liquidity is scarce. LPs with higher tolerance for liquidity risk will realize higher average returns compared to other LPs, and the difference is larger when liquid capital is more scarce. The introduction of a secondary market can lead to market segmentation, where LPs facing lower liquidity risk switching to the secondary market and those with higher liquidity risk staying in the primary market.