This is a textbook for postgraduate students and researchers on the theory of asset pricing and portfolio selection in multi-period settings under uncertainty. The asset pricing results are based on three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality and equilibrium. These results are unified with two key concepts, state-prices and martingales. Technicalities are given relatively little emphasis so as to draw connections between these concepts and to make plain that the similarities between discrete and continuous-time models are based on Brownian motion. Examples include the Black-Scholes option pricing model, Lucas' single-agent Markov asset pricing model, Merton's problem of optimal portfolio and consumption choice in a continuous-time setting, the Harrison-Kreps theory of equivalent martingale measures, Breeden's consumption-based capital asset pricing model, and the term structure model of Cox, Ingersoll and Ross. Numerical solution techniques include "binomial" methods, Monte Carlo simulation and finite-difference methods for solving partial differential equations. Each chapter provides extensive problem exercises and notes to the literature.