This book is about the stock market. The topics covered in the book include technical analysis, valuation theories, price ratios, portfolio analysis, the discount rate, and options. The language of mathematics is used widely in the book so that these topics and their results can be stated precisely. The mathematical results used in the book are collected in a single chapter titled, Mathematical Preliminaries. The book contains a number of observations about the stock market, including the following:1) Historically, the stock market has proved to be an effective hedge against the risk of inflation.2) The Central Limit Theorem, when applied to the historical inflation data, indicates that the probability of deflation is now higher than that of inflation.3) The claim that it is impossible to beat the S&P 500 index in the long run can be established as a mathematical result.4) The practical reliability of the Capital Asset Pricing Model (CAPM) beta calculation is questionable even with a large number of data points, as the model is not robust.5) If one assumes that the price of a stock is a random walk, then there are natural stop-loss and take-profit prices based on certain limiting probabilities.These and other observations in the book are illustrated with numerous examples.