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The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is a fundamental problem. This book offers a look at resolutions. Explaining the tools needed for understanding resolutions, it explains the history and ideas, providing an insight and intuition for the novice.

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved....