There was a School and Conference on Algebraic K-theory and its applications from May 14 to June 1, 2007. The first two weeks, May 14-25, were devoted to the School while the Conference took place May 28 - June 1. This volume contains the expository lectures given at the School. The School and Conference was a follow-up to the earlier ones in 1997 and 2002. The Proceedings of the 1997 School and Conference was published by World Scientific in 1999. The 2002 School and Conference was dedicated to Hyman Bass on the occasion of his seventieth birthday. The Proceedings of the School appeared in the ICTP Lecture Notes Series, while the Proceedings of the Conference appeared in a special issue of the journal “K-Theory” in 2003. These schools and conferences have emphasized the multidisciplinary nature of algebraic K-theory. Indeed, K-theory has become part of the fabric of Algebra, Algebraic Geometry, Analysis, Number Theory, and Topology. K-theory has brought new techniques and structures to these subjects, enabling fundamental contributions. The lectures presented here were given in order to introduce some of the fundamental aspects of Algebraic K-theory and to present important current connections with topics such as the Bloch-Kato Conjecture, motivic cohomology and quadratic forms. The six topics of the lecture series are as follows: (1) Introduction to K-theory; (2) Linear algebraic groups and K-theory; (3) K-theory and quadratic forms; (4) Motives; (5) Proof of the Bloch-Kato conjecture and (6) K-theory and non-commutative algebraic geometry. (ISBN 92-95003-38-1)