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...Lecture notes an introduction to riemannian geometry version december sigmundur gudmundsson lund university the latest of this document can be obtained at http www matematik lu se matematiklu personal sigma index html preface these grew out m sc course on dierential which i gave leeds their main purpose is introduce beautiful theory a still very active research area mathematics subject with no lack interesting examples they are indeed key good understanding it and will therefore play major role throughout work special interest classical lie groups allowing concrete calculations many abstract notions menu study rather meaningless without some basic knowledge gaussian that curves surfaces in dimensional space for we recommend excellent textbook p do carmo ge ometry prentice hall written students under standing linear algebra real analysis several variables clas sical ordinary equations topology most important results stated text also proved there other smaller ones left reader as exercis...