A seminar on Motivic Cohomology took place at the Centro de Investigaci´on en Matem´aticas (CIMAT), at Guanajuato (M´exico) during the month of August 2010. The aim of the seminar was to cover the definition and main properties of motivic cohomology of smooth schemes over a perfect field as defined by V. Voevodsky, and its relation to ´etale cohomology, Bloch’s higher Chow groups and Milnor’s algebraic K-theory, based on the book [MVW]. The seminar was addressed to an audience with a basic knowledge of algebraic geometry and classical motives. It was not possible to cover all proofs of the different results presented along the sessions of the seminar, but we think that it emerged a clear picture of the subject. We thank all participants by their enthusiasm and specially Abd´o Roig, who has read a first draft of this report and contributed with his remarks. The seminar began on August 2 and ended on September 1. It consisted of ten sessions of one hour and a half according to the following programme and speakers.