I. Introduction  
II. Preliminaries  
A. Privacy and Performance Gains of Quantum Channels  
B. Communication over a Quantum Channel  
C. Formal Model  
D. Quantum Channel Capacity  
E. Definitions  
F. Geometrical Interpretation of the Density Matrices  

III. Classical Capacities of a Quantum Channel  
A. Extended Formal Model  
B. Capacity of Classical Channels  
C. Transmission of Classical Information over Noisy Quantum Channels  
D. The Private Classical Capacity  
E. The Entanglement-assisted Classical Capacity  
F. The Classical Zero-Error Capacity  
G. Entanglement-assisted Classical Zero-Error Capacity  
H. Related Work  

IV. The Quantum Capacity of a Quantum Channel  
A. Preserving Quantum Information  
B. Connection between Classical and Quantum Information  
C. The Lloyd-Shor-Devetak Formula  
D. The Assisted Quantum Capacity  
E. The Zero-Error Quantum Capacity  
H. Related Work  

V. Quantum Channel Maps and Capacities  
A. Channel Maps  

VI. Practical Implementations of Quantum Channels  
A. Acting Time in Asymmetric Channels  
B. Quantum Network Coding for Entanglement Distribution  

VII. Conclusions