ELAZ-Conferences (abbreviated from Elementare und Analytische Zahlentheorie) is a series of conferences devoted to elementary and analytic number theory. The first conference in the series was organized in 2000 by L. Lucht at the Technische Universität Clausthal. This proceedings contains talks and adapted versions of talks presented at the third conference in this series. It was organized by W. Schwarz and J. Steuding (both from Goethe-Universität Frankfurt/Main). At the conference 41 talks were delivered. The proceedings contains 22 papers and one obituary for Thomas Maxsein (1953-2004). The scope of the proceedings is wide and contains contributions ranging from the Goldbach problem, the Waring problem, the zeta function and L-series, arithmetic semigroups, exponential sums, arithmetic functions and the uniform distribution, to probabilistic number theory. Most of the presented papers are research contributions. The volume also contains surveys, for example on estimates of Fourier coefficients of Siegel cusp forms (K. Bringmann), lattice points in large regions and related arithmetic functions (A. Ivić, E. Krätzel, M. Kühleitner and W.G. Nowak), recent results on the Goldbach conjecture (J. Pintz) and ABC for polynomials, dessins d’enfants, and uniformization (J. Wolfart). The book is printed with great care and is worth browsing and reading for anyone interested in elementary and analytic number theory or to people looking for fresh research impetus in this quickly developing branch of mathematics.