DescriptionEmbedding theorems play a fundamental role in differential geometry, some of the theorems use extrinsic information to construct the embedding, while some solely use intrinsic one, hence are canonical. In this thesis, for any n-dimensional compact Riemannian Manifold M with smooth metric g, by using the heat kernel embedding, we construct a canonical family of conformal embeddings C_{t,k}: M--->R^{q(t)}, with t>0 sufficiently small, q(t)>> t^{-n/2}, and k as a function of O(t^l) in proper sense. The canonical property of the embeddings is preserved by finding all the conformal ones, which are the major differences from the isometric case.