Here is an 46 MB scan of the book. It's essentially out of print, but you might be able to get it for "only" $64.95 from Amazon.com.
MR0681120 (84m:14032) This revised edition is an excellent and very readable introduction to some basic notions in algebraic geometry. Reviewed by Reinhard Bölling
 This is a review of first edition. It was in German, but I ran it through the Alta Vista translator, with hillarious results (e.g., "the Hurwitz' sex formula"). It begins with a short introduction to valuation theory and gives Weil's proof of the sentence of Riemann smelling. The chapter closes with the Hurwitz' sex formula. In the second chapter Riemann surfaces are examined. First the local Uniformisierungssatz is proven and dealt then with the topology and the analytic structure of the Riemann surfaces. Thus it is shown among other things that the Riemann surfaces are being connected, triangulierbar and orientable. Finally with the integration on Riemann surfaces is dealt and the Cauchy sentence is proven. On this basis in chapter III the sentence is treated from Abel Jacobi (proof after Artin). Remarks over the Riemann relations and the Pontrjagin duality complete the chapter. In the next chapter the linear theory of the theta functions is represented (after the Weil Bourbakivortrag from the year 1949). Thus among other things that there is a normalized theta function in each equivalence class of theta functions, abelsche functions will become shown introduced and it the sentence by Riemann smelling for the torus are proven. Further one finds the sentence of Lefschetz over the projektive imbedding by a notdegenerated theta function. In an appendix to the illustration of the 1dimensionale case is implemented. To this chapter remarks over duality theory (binary abelsche variousnesses, Tate group in connection with rational and $p$ adischen representations, grief mating) close. In the end the connection is examined by theta functions and divisors. It is e.g. shown that the positive divisors on the torus can be represented by theta functions on #C^n$. The available book gives a very beautiful introduction to the theory of the abelschen functions. It will become little special knowledge presupposed and the proofs very in detail and easily understandably represented. This connected representation of the results is well suitable for students or as basis for lectures or seminars. Reviewed by Gerhard Pfister
