'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, the campers decided to sleep outside under the stars and not use their tents."
"However, we decided to lower our operating cost."
"Nevertheless, if we order take-out food we won't be able to stop working tonight."
"Nevertheless, the time-share condominium was a good investment."
"Nonetheless, the bankers are convinced they can succeed in the restaurant business."
"Nonetheless, we are going to implement safety procedures."