As would be expected, the first lecture is an introduction to the material and outlines aspects of his approach and also explains why the subject matter is important. He also spends some time thanking his hosts in a self deprecating manner. At the time, America (even in Harvard) was not the center of intellectual thought, so William James talks about the great honor given to him to share his thoughts to a European audience.
To start with, he outlines two methods of inquiry; the first attempts to determine the what and the second tries to answer why it is significant or valuable. For example, in Biblical studies, Historical Criticism tries to determine the history of the Bible and how it came together. Who were the original authors and how were the individual writings compiled together into a single document? However Historical Criticism can never determine value by itself. If your definition of value is that the document has to be perfect, consistent, and without error, then the Bible would not fare to well. I found it interesting how much has not changed in the last 100 plus years. He could have written the same words today and it still is very applicable.
He spent some time criticizing over simplistic determinations of causal links, for example a link to religion from human sexuality. But he was also concerned that religious experience was being dismissed because of their physical origin. He argues that you can't dismiss an experience because it was likely caused by epileptic seizures. The true measure of the value our its results; not where it came from. Of course that means we will never be able to immediately know the answer, but will have to wait. This goes against our human desires for easy answers.