Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly so they don't get "lost" when studying and reviewing. 
First, he gets students engaged in the study of mathematics by highlighting truly relevant, unique, and engaging applications. He explores math the way it evolved: by describing real problems and how math explains them. In doing so, it answers the question "When will I ever use this?"  
Then, Blitzer keeps students engaged by ensuring they don't get lost when studying. Examples are easy to follow because of a three-step learning system - "See it, Hear it, Try it" embedded into each and every one. He literally "walks" the student through each example by his liberal use of annotations - the instructor's "voice" that appears throughout.