This textbook provides a comprehensive foundation for developing asset-pricing models with heterogeneous investors. Volume I in a two-volume set, this book covers topics such as stochastic calculus, dynamic programming, representative agent models, and a numerical method (finite difference) for solving them. The book takes a step-by-step approach, carefully show the underlying object of the models and the implementation of the finite difference method and Upwind scheme to solve dynamic programming problems in asset pricing. Where appropriate, chapters include MATLAB code for ease of replication. This book will be of interest to advanced undergraduate and graduate students of finance, economics, mathematics, and statistics.