The good folks at Live Lingua have amassed quite an archive of the US Foreign Service Institute's (FSI) public domain (free!) language courses. Included and available for instant free download online is the US Foreign Service Institute's Swahili Language Course.
These free FSI Swahili lessons are just one of the dozens of foreign languages available. The FSI has developed language educational materials for decades and the more current ones are truly gems for language learners as they are focused on fast learning for practical situations. Some of the older materials are dated but still provide a lot of learning fodder at no cost.
This free Swahili course material was created by the FSI to give their foreign service teams quick and effective language training in regions where the Swahili language is spoken. It includes Swahili audio lessons and associated text documents for a complete beginner's Swahili course.