Recommended literature

Basics of étale cohomology:

• G. Tamme,  Introduction to étale cohomology. Springer, 1994
• J. Milne, Étale cohomology. Princeton University Press, 1980
  
• J. Milne, Lectures on étale cohomology
  
• L. Fu,  Étale cohomology theory. World Scientific Publishing Company, 2011
  
• Deligne et. al,  SGA 4.5. Springer, 1977
  

The Weil conjectures:

• P. Deligne, La conjecture de Weil I, Publ. Math. I.H.E.S 43 (1974), 273-307.
• E. Freitag, R. Kiehl, Etale cohomology and the Weil conjectures, Springer, 1988.
• J. S. Milne, Lectures on étale cohomology
• E. Kowalski, Trying to understand Deligne’s proof of the Weil conjectures

Crystalline cohomology and the Katz conjecture:

• P. Berthelot, A. Ogus, Notes on crystalline cohomology. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978.
• A. Grothendieck, Crystals and the de Rham cohomology of schemes. 1968 Dix Exposés sur la Cohomologie des Schémas pp. 306–358 North-Holland, Amsterdam; Masson, Paris 
• L. Illusie, Complexe de de Rham-Witt et cohomologie cristalline. Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 4, 501–661. 
• B. Mazur, Frobenius and the Hodge filtration (estimates). Ann. of Math. (2) 98 (1973), 58–95.
  

The Fontaine-Mazur conjecture and p-adic Galois representations:

• Olivier Brinon, Brian Conrad: CMI Summer School Nones on p-adic Hodge Theory
  
• Jean-Marc Fontaine, Yi Ouyang: Theory of p-adic Galois Representations
• J-M. Fontaine and B. Mazur, Geometric Galois Representations, Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), 41–78, Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995.
• G. Faltings, Crystalline cohomology and p-adic étale cohomology, Algebraic analysis, geometry and number theory, The John Hopkins Univ. Press, 1989, pp. 25–80.
• M. Kisin, The Fontaine-Mazur conjecture for GL₂. J. Amer. Math. Soc. 22 (2009), no. 3, 641–690.