'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, she decided to continue with an optical storage system."
"However, the encryption program was based on a system lifted from the back of a cereal box."
"Nevertheless, we increased our rate of output."
"Nevertheless, if we provide ergonomic equipment our employees won't necessarily be more comfortable."
"Nonetheless, we are going to install an expansion card."
"Nonetheless, we are going to continue to implement SEO tactics and increase our page ranking."