Your choice to leave or stay depends on a number of factors. In deciding whether or not to give your spouse a second chance, I'd encourage you to ask the following questions. If you are able to say "yes" to the them, then there is obvious hope for your marriage's recovery. The presence of "no" answers means you need to be cautious before moving forward in your relationship. 

1. Is this the first time it's happened, or is it a pattern?
2. Is there an obvious shift toward honesty, or are there still cover-ups and lies?
3. Does their confession include information you did not know, or only admitting to what you found out?
4. Does your spouse show genuine remorse for the behavior, or just sorry for getting caught?
5. Does your spouse accept full responsibility, or make excuses?
6. When confronted with your pain, does your spouse respond with empathy, or defensiveness?
7. Is your spouse willing to do the work of repairing trust, or are you expected to just get over it?
8. Does your spouse have insight into their affair behavior, or do they just call it a big mistake?

It all comes down to making one of three choices: You can leave immediately; you can give it some time and see if things change; you can decide that the choice to end your marriage will have to be your spouse's decision, not yours. For a complete consideration of these options, read the full article: Should I Stay or Should I Go?