'However', 'nevertheless', and 'nonetheless' connect two sentences and show an unexpected result to what has been stated in the preceding sentence. 'However' is the most common of these expressions, whereas 'nevertheless' and 'nonetheless' are more formal are generally used in written English.
However, they decided to form a nonprofit organization."
However, the expenditures were higher than we expected and we had to shut down."
Nevertheless, if we break with the norm we won't be accepted."
Nevertheless, we can achieve sustainability if we for a company that is not just for profit."
Nonetheless, we are seeking assistance from a faith-based organization."
Nonetheless, I will only speak off the record."