1. Lecture 1: Systems Biology a. Introduction to Biology b. Regulatory & Metabolic Processes c. Algebraic Models in Biology 2. Lecture 2: Model Checking a. Temporal Logic b. Kripke Models c. Model Checking d. Biologically Faithful Models 3. Lecture 3: Semi-Algebraic Geometry a. Real Closed Field b. Tarski Algebra c. Decision Theories d. Hybrid Models e. Algorithmic Algebraic Model 4. Lecture 4: Hybrid Systems a. Hybrid Models b. Algorithmic Algebraic Models & Model Checking c. O-minimal Systems & SaCoRe d. IDA e. Open Problems