# put into my heart

"inspired me" or "led me" 

# to enroll them

"to list and register them"

# the book of the genealogy

This was a book that no longer exists. The people who returned from Persia were counted according to their families. Nehemiah ensured that those who lived in Jerusalem had a completely Jewish ancestry.

# found the following written in it

"found that someone had written the following in it"