  This monograph introduces the reader to basic notions of integrable
techniques for one-dimensional quantum systems. In a pedagogical way, a few
examples of exactly solvable models are worked out to go from the coordinate
approach to the Algebraic Bethe Ansatz, with some discussion on the finite
temperature thermodynamics. The aim is to provide the instruments to approach
more advanced books or to allow for a critical reading of research articles and
the extraction of useful information from them. We describe the solution of the
anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact
interaction at zero and finite temperature; and of the XXZ spin chain, first in
the coordinate and then in the algebraic approach. To establish the connection
between the latter and the solution of two dimensional classical models, we
also introduce and solve the 6-vertex model. Finally, the low energy physics of
these integrable models is mapped into the corresponding conformal field
theory. Through its style and the choice of topics, this book tries to touch
all fundamental ideas behind integrability and is meant for students and
researchers interested either in an introduction to later delve in the advance
aspects of Bethe Ansatz or in an overview of the topic for broadening their
culture.
