We propose a methodology for the specification, verification, and design of hybrid systems. The methodology consists of the computational model of Concrete Phase Transition Systems, the specification language of Hybrid Temporal Logic (HTL), the graphical system description language of Hybrid Automata, and a proof system for verifying that hybrid automata satisfy their HTL specifications. The novelty of the approach lies in the continuous-time logic, which allows specification of both point-based and interval-based properties (i.e., properties which describe changes over an interval) and provides direct references to derivatives of variables, and in the proof system that supports verification of point-based and interval-based properties. The proof rules demonstrate that sound and convenient induction rules can be established for continuous-time logics. The proof rules are illustrated on several examples.