This is a doctoral course examining advanced topics on portfolio choice and, especially, asset pricing. It is assumed that students have an MSc-level understanding of portfolio choice under uncertainly, asset pricing and portfolio theory, allowing the course to concentrate on an advanced treatment of these topics. We will not assume, however, previous exposure to doctoral courses in quantitative finance, financial economics and/or econometrics. In other words, this will be a foundational course in doctoral-level asset pricing. The overarching goal and my hope are that, upon completion of this course, students will be able to go on a journey of discovery of the recent research in asset pricing and will have the conceptual and intellectual tools to contribute to it, as well as to contribute to the dissemination of the insight of rigorous asset pricing to other areas of financial (e.g., corporate finance and risk management, banking) and economic (both micro and macro) research. Therefore, the priority will be to lay down foundations for serious scholarly research in asset pricing and for using asset pricing in autonomous scholarly research in other branches of Finance and Economics, rather than to survey all latest research articles (though we will discuss a good few of them). This means that we will have to devote considerable attention to the classics and to classic problems in portfolio choice and asset pricing. This is the only way to properly understand what recent research is up to. In the process, we will have the opportunity to build intuition and shed light on key properties of important and familiar estimators. For example, we will discover that OLS, Maximum Likelihood and panel estimators are all special cases of GMM. Perhaps more importantly, we will gain familiarity with proofs. The aim will be to get students used to read, understand and adapt proofs and, possibly, make them confident enough to develop their own proofs from scratch. More generally, the rigor of asset pricing theory should help students develop the ability to better structure their arguments. The main theoretical framework of the course is the ongoing revolution in Finance that has gradually replaced static, overly stylized asset pricing and investment evaluation models with richer ones. These new models recognize the complexities of the investment problem and of how economic agents solve it (or attempt to do so). The unifying theme will be the role of stochastic discount factors (or pricing kernels) in linking asset prices to asset payoffs. We will learn how they can be used to represent the implications of asset pricing models in different setting (complete and incomplete markets, with or without frictions and over one or more periods). It will be fun to discover how easily (in two lines) familiar models involving risk factor loadings (e.g., the market beta) and risk premia (e.g., the market risk premium) pop out from models expressed in terms of a given stochastic discount factor. Increasingly it is hard to miss the implications of advanced asset pricing for advanced portfolio management, and the lessons the practitioners of the former can gain from the practitioners of the latter. Therefore, the course will treat portfolio choice and asset pricing in a unified manner. Please keep your laptop ready for action as it will be needed for empirical applications, which are essential to shed light on the theory, how it has developed and the challenges it faces. I expect most students will have access to Matlab and, therefore, the code that I will make available will be mostly for use in Matlab but I will do my best to support also other programming languages (I know R well, which is a good substitute for Matlab) and some of the work can be at least fruitfully prototyped in MS Excel (an excellent learning tool). Students are encouraged to read the reference material in the textbook before the lecture.