This volume covers many topics including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. This book contains many interesting theoretical and applicated new results and surveys presented by the best specialists in these areas, such as new results on Serre's questions, answering a question in his letter to Top; new results on cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperellyptic curves, including computation of the discrete logarithm; new results on function field towers; the construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.