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This work is concerned with the analysis of the conditions for a map-germ to be finitely determined and of the degree of determinacy. In Chapters II and III, we obtain estimates for the degree of C^r-G-determinacy, where G = K,R and C. These estimates are exact in many cases, as for instance, in the following proposition: "Let f : (Rⁿ, 0) → (R^p,0) be given by: {u_i = x_i i = 1, ..., p-k, y_j = f_{j (x1, ... xp-k, xp-k+1, ..., xn), j = 1, ... k, where fj is homogeneous of degree sj. If f is G-determined or more generally if IG is elliptic then f is (s+l-1)-C^l-G determined, with s = max sj". The groups of interest in Chapters IV and V are A and C⁰-A. We obtain relations among tangent spaces to the orbits,and we apply them to problems of topological triviality, modality and normal forms, The main result in Chapter IV is a sufficient condition for topological triviality, that applies to map-germs not necessarily weighted-homogeneous. In Chapter V we deal with A-finitely determined germs with the property that the A-orbit is open in the K-orbit. As an application of the results, we obtain the classification of all f : (R²,0) → (R²,0) of type Σ¹ and Σ², 0 having that property.}