This volume collects the lectures of Grothendieck's seminar at the IHES in 1965-66, originally distributed as mimeographed notes. The only significant changes from the original version are that lecture II is not included and lecture III has been completely rewritten and expanded with an appendix III B. Other lectures have been left unchanged except for minor modifications and additions of footnotes. The core of the seminar is the Lefschetz formula in étale cohomology (III, III B, XII) and its application to the cohomological interpretation of L-functions (XIV). All results announced by Grothendieck in his Bourbaki talk [2] are fully proved here. The trace formulas established in (III, III B, and XII), through different paths, are more general than needed to prove the rationality of L-functions. A shorter, more complete proof of this, following Grothendieck's method from lectures XII and XIV, is given in Deligne's lecture (SGA 41/2 Rapport). We hope that the formulas in III, III B may be useful in other situations. The rest of the seminar consists of two lectures on the theory of limits leading to étale cohomology (V, VI), and various complements to duality formalism (I, VII) and the Lefschetz formula (VII, X). Lecture I is independent of the rest of the seminar. Its main result is that, on a regular scheme satisfying certain local conditions, and provided that one has the resolution of singularities and purity theorem, the constant sheaf of values Z/nZ, for n prime to the residual characteristic, is dualizing (I.3.4.1). This theorem applies particularly to excellent regular schemes of characteristic zero, thanks to Hironaka and Artin's results (SGA 4 XIX). The case of a regular scheme of dimension 1 is treated separately, by another method, which is very elementary (see also (SGA 41/2 Dualité)). Lecture II, which was titled "Künneth formulas for cohomology with arbitrary supports," is not included in this volume. Written by L. Illusie, based on handwritten notes by Grothendieck, it was devoted to theorems of cohomological properness and local acyclicity, but these were only proved under resolution hypotheses. A proof of the same results without these hypotheses, obtained by Deligne (SGA 41/2 Th. Finitude), has made the publication of this lecture unnecessary. Some complements, concerning for example the case of divisors with normal crossings, have been incorporated into an appendix to (loc. cit.). It is also noted that analogous theorems for the case of sheaves of sets and non-commutative groups are proved in the lecture by MThis volume collects the lectures of Grothendieck's seminar at the IHES in 1965-66, originally distributed as mimeographed notes. The only significant changes from the original version are that lecture II is not included and lecture III has been completely rewritten and expanded with an appendix III B. Other lectures have been left unchanged except for minor modifications and additions of footnotes. The core of the seminar is the Lefschetz formula in étale cohomology (III, III B, XII) and its application to the cohomological interpretation of L-functions (XIV). All results announced by Grothendieck in his Bourbaki talk [2] are fully proved here. The trace formulas established in (III, III B, and XII), through different paths, are more general than needed to prove the rationality of L-functions. A shorter, more complete proof of this, following Grothendieck's method from lectures XII and XIV, is given in Deligne's lecture (SGA 41/2 Rapport). We hope that the formulas in III, III B may be useful in other situations. The rest of the seminar consists of two lectures on the theory of limits leading to étale cohomology (V, VI), and various complements to duality formalism (I, VII) and the Lefschetz formula (VII, X). Lecture I is independent of the rest of the seminar. Its main result is that, on a regular scheme satisfying certain local conditions, and provided that one has the resolution of singularities and purity theorem, the constant sheaf of values Z/nZ, for n prime to the residual characteristic, is dualizing (I.3.4.1). This theorem applies particularly to excellent regular schemes of characteristic zero, thanks to Hironaka and Artin's results (SGA 4 XIX). The case of a regular scheme of dimension 1 is treated separately, by another method, which is very elementary (see also (SGA 41/2 Dualité)). Lecture II, which was titled "Künneth formulas for cohomology with arbitrary supports," is not included in this volume. Written by L. Illusie, based on handwritten notes by Grothendieck, it was devoted to theorems of cohomological properness and local acyclicity, but these were only proved under resolution hypotheses. A proof of the same results without these hypotheses, obtained by Deligne (SGA 41/2 Th. Finitude), has made the publication of this lecture unnecessary. Some complements, concerning for example the case of divisors with normal crossings, have been incorporated into an appendix to (loc. cit.). It is also noted that analogous theorems for the case of sheaves of sets and non-commutative groups are proved in the lecture by M