I. INTRODUCTION

II. PARAMETERIZING MODIFIED GRAVITY
A. Parameterizing gravitational potentials in discrete redshift bins
B. Parameterizing gravitational potentials with simple smooth functions of the scale factor

III. THE POWER SPECTRUM IN MODIFIED GRAVITY
B. Non-linear power spectra

IV. FISHER MATRIX FORECASTS
A. Future large scale galaxy redshift surveys
B. Galaxy Clustering
C. Weak Lensing
D. Covariance and correlation matrix and the Figure of Merit
E. CMB Planck priors

V. RESULTS: EUCLID FORECASTS FOR REDSHIFT BINNED PARAMETERS
A. Euclid Galaxy Clustering Survey
B. Euclid Weak Lensing Survey
C. Combining Euclid Galaxy Clustering and Weak Lensing, with Planck data
D. Decorrelation of covariance matrices and the Zero-phase Component Analysis

VI. MODIFIED GRAVITY WITH SIMPLE SMOOTH FUNCTIONS OF THE SCALE FACTOR
A. Modified Gravity in the late-time parameterization
B. Modified Gravity in the early-time parameterization
C. Testing the effect of the Hu-Sawicki non-linear prescription on parameter estimation

VII. CONCLUSIONS