Course texts:
"The study of toric varieties is a wonderful part of algebraic geometry that has deep connections with polyhedral geometry. Our book will be an introduction to this rich subject that assumes only a modest knowledge of algebraic geometry. There are elegant theorems, unexpected applications, and marvelous examples that illustrate the scope and power of modern algbraic geometry."
And here is a perspective on toric varieties taken from Fulton's book:
"Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories."