1 General Principles.- 2 the Radiation Field.- 3 Relativistic Theory of Free Electrons.- 4 Interaction of Radiation with Electrons.- 5 Invariance Properties of the Coupled Fields.- 6 Subsidiary Condition and Longitudinal Field.- 7 the S-Matrix.- 8 Evaluation of the S-Matrix.- 9 the Divergences in the Iteration Solution.- 10 Renormalization.- 11 the Photon-Electron System.- 12 the Electron-Electron System.- 13 the Photon-Photon System.- 14 Theory of the External Field.- 15 External Field Problems.- 16 Special Problems.- Mathematical Appendix.- Appendix A1 the Invariant Functions.- A1-1 The homogeneous delta-functions.- A1-2 The inhomogeneous delta-functions.- A1-3 Relations between the ?-functions.- A1-4 Integral representations.- A1-5 Explicit expressions.- A1-6 The S-functions.- Appendix A2 the Gamma-Matrices.- A2-1 Various representations.- A2-3 The amplitudes of the plane wave solutions.- A2-5 Spin sums.- A2-6 Polarization sums.- Appendix A3 a Theorem on the Representation of the Extended.- Lorentz Group by Irreducible Tensors.- Appendix A4 the Ordering Theorem.- A4-1 The ordering theorem for commuting fields.- A4-2 The ordering theorem for anticommuting fields.- A4-3 A generalization of the ordering theorem.- A4-4 The ordering of chronological products.- Appendix A5 on the Evaluation of Certain Integrals.- A5-1 Convergent integrals.- A5-2 Divergent integrals.- A5-3 The integral for the photon self-energy part.- A5-4 The integral for the electron self-energy part.- Appendix A6 a Limiting Relation for the ?-function.- Appendix A7 the Method of Analytic Continuation.- A7-1 The Bohr-Peierls-Placzek relation.- A7-2 The principle of limiting distance.- A7-3 The fundamental theorem on analytic continuation.- A7-4 Applications.- Appendix A8 Notation.- Supplement for theSecond Edition.- Supplement S1 Formulations of Quantum Electrodynamics.- S1-1 Lagrangian QFT.- S1-2 Axiomatic QFT.- S1-3 Locality, covariance, and indefinite metric.- S1-4 Lehmann-Symanzik-Zimmermann and related formalisms.- S1-5 Null plane QED.- References.- Supplement S2 Renormalization.- S2-1 Dyson-Salam-Ward renormalization.- S2-2 Bogoüubov-Parasiuk-Hepp-Zimmermann renormalization.- S2-3 Analytic renormalization.- References.- Supplement S3 Coherent States.- S3-1 A finite number of degrees of freedom.- S3-2 Coherent states of the radiation field.- S3-3 Application to ordering theorems.- References.- Supplement S4 Infrared Divergences.- S4-1 Dollard's discovery.- S4-2 A new picture.- S4-3 The asymptotically modified fields.- References.- Supplement S5 Predictions and Precision Experiments.- S5-1 The anomalous magnetic moment.- S5-2 The hyperfine structure of the hydrogen ground state.- S5-3 The Lamb-Retherford shift in hydrogen.- S5-4 Energy levels in positronium.- S5-5 Muonium hyperfine structure.- References.- Author Index.