Which European explorer is known for his extensive travels in East Africa, particularly along the course of the Nile River and the discovery of Lake Victoria?

The European explorer known for his extensive travels in East Africa, particularly along the course of the Nile River and the discovery of Lake Victoria, is John Hanning Speke.

Here are the steps to answer this question:

1. Identify the key points in the question: European explorer, extensive travels in East Africa, Nile River, and discovery of Lake Victoria.

2. Use these key points to search for the answer. In this case, the answer is well-known in the field of history, so it's not necessary to do a search.

3. John Hanning Speke was a British explorer. He is most associated with the exploration of East Africa and the discovery of Lake Victoria, which he named. He believed it to be the source of the Nile, and he was eventually proven correct.

4. Therefore, the answer to the question is John Hanning Speke.