Multi-Period Trading via Convex Optimization considers a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. It describes a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. It then describes a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single period method traces back to Markowitz; the multi-period methods trace back to model predictive control. This monograph addresses the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. The methods described can be thought of as good ways to exploit predictions, no matter how they are made. Multi-Period Trading via Convex Optimization collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework. It provides the reader with a unified, self-contained treatment, focusing on the practical issues that arise in multi-period trading. It will benefit anyone interested in the study of these methods and is also an ideal reference for a quantitative trader, or someone who works with or for, or employs, one.