Sentence:  Definition 1.15. "Let G and H be matrix Lie groups. A map \Phi from G to H is called a <WSD>Lie group homomorphism</WSD> if (1) \Phi is a group <WSD>homomorphism</WSD> and (2) \Phi is continuous." 
Meaning of the word marked with <WSD> tags:  A structure-preserving (map) between two algebraic structures of the same type, such as (groups), (rings), or vector spaces.