An elementary and computationally explicit introduction to the theory of binary quadratic forms. Where possible, the emphasis is on explicit, algorithmically sensible proofs and examples. Constructive proofs are preferred over existence proofs. The author offers a contemporary discussion of the classical theory and a survey of computations and applications. The text should be understandable by advanced undergraduates in mathematics and computer science, and the expert in number theory will likely find the computational emphasis rewarding.

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