We present 18 Introductory Lectures on K-Theory covering its basic three branches, namely topological, analytic (K-Homology) and Higher Algebraic K-Theory, 6 lectures on each branch. The skeleton of t . . . . .

This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of som . . . . .

In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially descr . . . . .

Contenuto:Il formalismo della Meccanica Quantistica; Simmetrie in Meccanica Quantistica; Rappresentazioni unitarie; Gruppi di simmetria spazio-temporale.

This book is the main text for 15.053 Introduction to Optimization taught at MIT. To make the book available online, most chapters have been re-typeset. Chapters 6, 7 and 10 were not, but are still av . . . . .

Contents: The geometry of monoids; Log structures and charts; Morphisms of log schemes; Differentials and smoothness; De Rham and Betti cohomology.