Abstract: Conformal Geometric Algebra （CGA） is a new tool for geometric representation and computation.As an integration of advanced geometric invariants and covariants systems,CGA provides a unified and compact homogeneous algebraic framework for classical geometries,together with a set of effective algorithms for expansion,elimination and simplification,which enables it to carry out extremely complicated symbolic geometric computations,and be used quite advantageously in geometric modeling and computing. This is the first of a series of papers dedicated to the introduction of CGA.The paper focuses on the background and importance of CGA,the mathematical theory and several most important features,including the Grassmann structure,the universal geometric representation and spin or action,the basic invariant system and advanced invariant system,the new idea in computing,the expansion and simplification techniques, etc.