Those notes shape the contents of a Nachdiplomvorlesung given on the Forschungs institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. okay. Chandrasekharan and Prof. Jurgen Moser have inspired me to put in writing them up for inclusion within the sequence, released by way of Birkhiiuser, of notes of those classes on the ETH. Dr. Albert Stadler produced specific notes of the 1st a part of this path, and intensely intelligible class-room notes of the remaining. with out this paintings of Dr. Stadler, those notes wouldn't have been written. whereas i've got replaced a few issues (such because the facts of the Serre duality theorem, the following performed totally within the spirit of Serre's unique paper), the current notes persist with Dr. Stadler's quite heavily. My unique objective in giving the path used to be twofold. i needed to offer the fundamental theorems in regards to the Jacobian from Riemann's personal standpoint. Given the Riemann-Roch theorem, if Riemann's tools are expressed in sleek language, they fluctuate little or no (if in any respect) from the paintings of recent authors.
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