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These notes are devoted to the theory of exponential sums over finite fields.The first chapter recalls some of the number-theoretic interest of such sums.The second chapter discusses the $L$-functions attached to such sums, the "Weilconjectures" for these $L$-functions as established by Deligne, andtheconsequences for the exponential sums themselves. The third chapter is devotedto the cohomological interpretation of exponential sums and of their associated$L$-functions. These first three chapters are largely of an expository nature.  The main results are found in chapters four and five. Chapter four is devotedto theorems of uniformity "for almost all $p$" for the cohomological structureof quite general exponential sums. Chapter five is devoted to a preciseanalysis of the cohomological structure of certain specific classes ofexponential sums for which the associated algebro-geometric situation isespecially attractive.

A translation of N.M. Katz's "Exponential Sums"