This book is intended for use in a rigorous introductory Ph.D.-level course in econometrics or in a field course in econometric theory. It is based on lecture notes that I developed during the period 1997–2003 for the first-semester econometrics course “Introduction to Econometrics” in the core of the Ph.D. program in economics at the Pennsylvania State University. Initially, these lecture notes were written as a companion to Gallant's (1997) textbook but have been developed gradually into an alternative textbook. Therefore, the topics that are covered in this book encompass those in Gallant's book, but in much more depth. Moreover, to make the book also suitable for a field course in econometric theory, I have included various advanced topics as well. I used to teach this advanced material in the econometrics field at the Free University of Amsterdam and Southern Methodist University on the basis of the draft of my previous textbook (Bierens 1994).

Some chapters have their own appendixes containing the more advanced topics, difficult proofs, or both. Moreover, there are three appendixes with material that is supposed to be known but often is not – or not sufficiently. Appendix I contains a comprehensive review of linear algebra, including all the proofs. This appendix is intended for self-study only but may serve well in a half-semester or one-quarter course in linear algebra. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews the basics of complex analysis, which is a subject needed to understand and derive the properties of characteristic functions.