1 Introduction  
1.1 Motivation  
1.2 Structure  
1.3 "There Be Dragons" - traps to be avoided when going from frame theory to fusion frame theory  

2 Preliminaries  
2.1 Frame theory  

3 Fusion frames  

4 Other notions in fusion frame theory  

5 Fusion frames and operators  

6 Duality in fusion frame theory  
6.1 $\varrho$-dual fusion frames  
6.2 Block-diagonal and component preserving $\varrho$-dual fusion frames  
6.3 Dual fusion frame systems  
6.4 Relation between block-diagonal dual frames, dual fusion frame systems and dual frames  
6.5 Dual families  
6.6 The canonical dual fusion frame  
6.7 Summary of properties of dual fusion frames  
6.8 Examples of dual fusion frames  
6.9 Particular choices of $\varrho$  

7 Finite fusion frames  
7.1 Fusion frames in finite-dimensional Hilbert spaces  

8 Reproducible research implementations  
8.1 Dual fusion frame calculation  
8.2 Towards the Visualization of Fusion Frame Coefficients  
8.3 Fusion Frames with a Time-Frequency Relation  

9 Further study