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The book offers a comprehensive introduction to algebraic geometry, beginning with fundamental concepts such as affine and projective varieties, along with key attributes and examples. The second part delves into the theory of curves, exploring local properties, affine and projective plane curves, and the resolution of singularities. It also covers important topics like linear equivalence of divisors, linear series, and the Riemann-Roch and Riemann-Hurwitz Theorems, providing a thorough understanding of both foundational and advanced topics in the field.

This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry. The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.