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This is the first part of a guide to deformations and moduli, especiallyviewed from the perspective of algebraic surfaces (the simplest higherdimensional varieties). It contains also new results, regarding the question oflocal homeomorphism between Kuranishi and Teichmueller space, and a survey ofnew results with Ingrid Bauer, concerning the discrepancy between thedeformation of the action of a group G on a minimal models S, respectively thedeformation of the action of G on the canonical model X. Here Def(S) mapsproperly onto Def(X), but the same does not hold for pairs: Def(S,G) does notmap properly onto Def(X,G). Indeed the connected components of Def(S), in thecase of tertiary Burniat surfaces, only map to locally closed sets. The lastsection contains anew result on some surfaces whise Albanese map has genericdegree equal to 2.

A Superficial Working Guide to Deformations and Moduli