If you'd like to improve your German skills in a classroom setting, language schools are the right solution for you. Depending on your level and available hours, you'll find that there are many options in Hamburg to choose from. Please note that only certain language certificates are recognised when applying for a visa or a residence permit. More information can be found here: Proof of German language knowledge.
The Goethe-Institut is the official cultural institution of the Federal Republic of Germany. It encourages cultural exchange worldwide and also offers numerous German language courses tailored to your goals and preferences. Goethe-Institut offers intensive and evening courses from beginner to university level. Courses start once a month or every other week and can be booked for any period from two weeks to a whole year.
Adult Education Centre (Volkshochschule)
This public adult education institution offers numerous courses on all kinds of subjects, including courses in German as a Foreign Language (also available as online courses). The courses are usually scheduled in the evening and available at a very reasonable fee.
Language courses at commercial schools usually cost more than state-subsidised and non-profit courses. Courses are offered in a variety of different locations and levels throughout Hamburg. Commercial language schools can be found online in the internet business pages of Hamburg under the search term Sprachschule / Fremdsprachen Hamburg, for example.