To study you should try challenges yourself as well as read writeups about how people approached solving these types of problems.
Write ups from previous competitions:
https://ctftime.org/writeups
https://github.com/ctfs/write-ups-2014
Defcon CTF: https://www.defcon.org/html/links/dc-ctf.html
CSAW Archives:
2013: https://ctf.isis.poly.edu/static/archives/2013/writeups/index.html
2012: https://ctf.isis.poly.edu/static/archives/2012/writeups/index.html
Sample Problems
Brute force hash collision:
http://josephpcohen.com/teaching/cs210/hw8/
SQL Injections:
http://ringzer0team.com/challenges/1
http://ringzer0team.com/challenges/2
PHP and Linux
http://ringzer0team.com/challenges/75
http://ringzer0team.com/challenges/113
Now some XXS:
http://ringzer0team.com/challenges/96
http://web.ringzer0team.com:13376/xss1.php
Shellcode and Linux.
http://ringzer0team.com/challenges/127
ssh level1@shellcode.ringzer0team.com -p 7771
Exploit a programs memory
http://ringzer0team.com/challenges/80
ssh level1@bin01.ringzer0team.com port 22
Forensics
http://ringzer0team.com/challenges/89
I found there is mail running and stuff in log files. Cypher has some mail.
More:
http://ringzer0team.com/challenges/109
http://io.smashthestack.org:84/
http://logic.smashthestack.org:88/