In one note to fellow scientist Michele Besso, Einstein confesses that after 50 years of dedication, he does not understand the quantum nature of light.
The collection also includes a letter in which Einstein expresses concern about the rise of the Nazi party in Germany.
Sent to his son Hans Albert in 1935, the letter reads: "Even in Germany things are slowly starting to change. Let's just hope we won't have a Europe war first."
The new collection joins more than 80,000 items in the Albert Einstein Archives including medals, diplomas and photographs.
Einstein was one of the founders of the university and donated his personal and scientific writing to create the Albert Einstein Archives.
The archives' academic director, Hanoch Gutfreund, said: "We at the Hebrew University are proud to serve as the eternal home for Albert Einstein's intellectual legacy, as was his wish."
In 2017, a letter by Albert Einstein in which he grapples with the concept of religion sold for nearly $2.9m (£2.3m).