1 INTRODUCTION  
2 LENSING FORMALISM  
3 METHODOLOGY  
3.1 Direct inversion  
3.2 Forward fitting approach  
3.3 Examining the reconstructions  
4 SIMULATIONS AND INITIAL TESTS  
4.1 Gaussian map tests  
4.2 Quantifying noise  
4.3 Galaxy survey simulations  
4.4 Moments  
4.5 PDF  
4.6 Minkowski functionals  
4.7 Comparing residuals  
5 DES Y1 RESULTS  
5.1 Data  
5.2 Weak lensing catalogues  
5.3 Redshift binning  
5.4 The DES Y1 fitted maps  
5.5 Systematics  
5.6 DES Y1 Minkowski functionals  
6 CONCLUSION