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In this work we delve into the theory of Chow-Heegner points, establishing some of their basic properties and developing two methods for their explicit computation. Chapters 1 and 2 cover the background material necessary for the later chapters. Chapter 3 gives several definitions of Chow-Heegner points and explores the specific setting of modular abelian varieties. Chapter 4 develops an algorithm for computing Chow-Heegner points via complex analytic methods, and Chapter 5 considers a corresponding algorithm in the p-adic setting.
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