Can't log into my email using Nexus 7 email client I want to use the email app on my Nexus 7 to access my university email. These email accounts are provided by Microsoft.

After I enter my account name, on the second screen, it asks me about Account Type. POP3, IMAP or Exchange.

I tried  


with POP3 > enter password > Incoming server settings(used defaults) > When trying to sign in "Couldn't finish : Couldn't open connection to server."
with IMAP, it asks for "sign in with password" or "sign in with google". In both cases, I get the error "Couldn't finish : Couldn't open connection to server"
with Exchange I get the same error. But in this case the email server asks for a "client certificate", I haven't selected anything for that option.


What are the options (POP3, IMAP, Exchange) and how to setup this email client for my university account?
You need to get this information from your university. Ask the IT department to walk you through it or just give you the necessary information.
From what you've said: 


  email accounts are provided by Microsoft.


seems to me they're using Exchange in a Windows domain (I could be wrong). Therefore, you'll need a server link, domain name, username, and password.

Also, on a separate note, you should do some research on how email works and email protocols (POP3, IMAP, SMTP, Exchange, Gmail, and so on). Here's a helpful link: Email protocols: POP, IMAP and MAPI