Topics on Real Analytic Spaces: Advanced Lectures in Mathematics

I Ringed Spaces.- § 1. k-ringed spaces.- § 2. Coherent sheaves.- § 3. Embeddings.- II Spaces and Varieties.- § 1. General properties.- § 2. Local properties.- § 3. Global properties.- § 4. Antiinvolutions.- III Complexification.- § 1. Complexification of germs.- § 2. Local complexification.- § 3. Global complexification.- IV Real Analytic Varieties.- § 1. Real part.- § 2. Analytic subvarieties.- § 3. Normalization.- § 4. Desingularization.- V Embeddings of Stein Spaces.- § 1. A first relative embedding theorem.- § 2. A second relative embedding theorem.- § 3. ?-invariant embedding theorems.- VI Embeddings of Real Analytic Varieties or Spaces.- § 1. Varieties: the general case.- § 2. Varieties: the pathological case.- § 3. The non reduced case.- § 4. Topologies on Cm(X, ?q).- VII Approximations.- § 1. The weak and strong topologies.- § 2. Approximations.- VIII Fibre Bundles.- § 1. Generalities on analytic fibre bundles.- § 2. A classification theorem.