I am behind on my mortgage and the bank has begun foreclosure proceedings... I want to do a quit claim, or transfer the title to the bank, as this will avoid the foreclosure, will it not?

Perhaps. Ask the bank if they will accept a deed in lieu of foreclosure, and then dismiss the foreclosure action.

Giving the bank a deed in lieu of foreclosure will stop the foreclosure action but it will still be on your credit report. Also, if the bank takes the deed and sells the property for less than the amount of the mortgage they can sue you for the balance. If they forgive the balance they will send you a 1099 and you will owe income taxes on the balance.

... Also, if the bank takes the deed and sells the property for less than the amount of the mortgage they can sue you for the balance. ...

A dismissal with prejudice of the foreclosure action (which no doubt seeks a deficiency judgment) would make them unable to do that.

But the bank will have to agree to take it, you can not just draw up the paper work and do this without the banks permission