Analog circuit design is traditionally done by expert designers in an ad hoc manner heavily dependent on simulation. This methodology has worked successfully for many years, but process variation and design complexity are prompting designers to explore new techniques. Formal methods are being used successfully to aid in the complex validation problem for digital circuits. This dissertation presents formal methods for analog and mixed-signal (AMS) circuits. This dissertation describes the development of a formal model, labeled hybrid Petri nets (LHPNs), appropriate for the modeling and verification of AMS circuits. An LHPN is a Petri net variant capable of modeling both continuous and discrete quantities. Creating an LHPN model of an AMS circuit by hand is a complicated and error prone exercise that requires expert knowledge. This is unacceptable for practical adoption of the LHPN model and its associated analysis methods. For this reason, this dissertation introduces an automatic LHPN model generation method. The method uses a set of simulation traces and a desired system property to generate an LHPN modeling the behavior of the simulation traces. The model generator can also be used to generate abstract Verilog-AMS or VHDL-AMS models suitable for use in system-level simulations. Formal verification of a property over the entire state space of an LHPN model is complicated by the infinite state of the model. For this reason, the infinite states of the model are grouped into potentially finite groups of equivalent states for verification. Difference bound matrices (DBMs), a restricted form of convex polygons, are used to represent these equivalent classes of infinite states. Reachability analysis using DBMs is very efficient at the cost of exactness. This dissertation presents algorithms for conservative state space analysis and verification of LHPNs. Finally, these methods are demonstrated on several case studies of AMS circuits from both academia and industry. The formal verification methods demonstrate the ability to find bugs missed by standard simulations. The abstract modeling methods show the promise of using automatically generated abstract models by demonstrating up to 40x speedup for some examples.