1 Introduction
1.1 Stochasticity in cosmological observables
1.2 Fisher information for cosmology: a first look
1.3 N-point functions
1.4 Gaussian and non-Gaussian matter density fields
1.5 Structure of the thesis

2 Shannon entropy and Fisher information
2.1 Fisher information and the information inequality
2.2 Jaynes Maximal Entropy Principle

3 Information within N-point moments
3.1 One variable
3.2 Several variables
3.3 Some exactly solvable models for moment determinate densities

4 On the combination of shears, magnification and flexion fields
4.1 Introduction
4.2 Linear tracers
4.3 Results

5 On the use of Gaussian likelihoods for power spectra estimators
5.1 Introduction
5.2 One field, gamma distribution
5.3 Several fields, Wishart distribution
5.4 Summary and conclusions

6 N-point functions in lognormal density fields
6.1 Introduction
6.2 Fundamental limitations of the lognormal assumption
6.3 Explicit fields with the same hierarchy of N-point functions
6.4 Information at all orders for the one dimensional distribution
6.5 Connection to N-body simulations
6.6 Information at all orders for uncorrelated fiducial
6.7 The general case: a difficult Lagrange interpolation problem

7 Information escaping the correlation hierarchy of the convergence field
7.1 Introduction
7.2 Fisher information coefficients
7.3 Restoration of the information
7.4 Conclusions