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There's more about databases in the database tab, but here are some quick links to get you started.
Web of Science
Indexes (including citation indexes) for over 8,500 leading journals.
Database of more than a million reviews and abstracts of math publications
Academic Search Premier (EbscoHost)
Provides full text for more than 4,600 journals, including full text for nearly 3,900 peer-reviewed titles. PDF backfiles to 1975 or further are available for well over one hundred journals, and searchable cited references are provided for more than 1,000 titles.