This is an introduction to quantitative finance based on a non-standard perspective called the "benchmark approach." This prices using "real world" probabilities and a "growth optimal portfolio" as numeraire. This approach offers a number of advantages over the traditional risk-neutral framework, but it is non-standard. While the book is written as an introduction, starting with basic concepts in probability theory, progressing through stochastic calculus and then developing financial concepts, the ideas presented in the second half of the book are likely to appeal primarily to theoreticians ...