There are four personal letters between Einstein and his friend Michele Besso and a letter to his son Hans Albert, who lived with Einstein's estranged wife in Switzerland.
The collection was recently donated to the university which hosts the largest collection of original documents written by the Nobel Prize victor.
Einstein helped establish Hebrew University and was a member of its board of directors.
Researchers are now preserving and digitizing the new documents, after which they will work to pick through the scientific and mathematical meanings for the calculations found within their margins.
The published materials include 84 manuscript pages containing mathematical derivations written between 1944 and 1948.
Gutfreund, a physics professor and former president of the university, said the eight-page appendix of the 1930 unified theory paper had never been published, though researchers had copies of it.
Einstein, who developed the theory of relativity, a pillar of modern science, tried unsuccessfully for decades to prove another concept - that electromagnetism and gravity were different manifestations of a single fundamental field.
Einstein himself moved from Germany to the United States in 1933 after the rise of Adolf Hitler.
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In the letter to his son, he writes that "in Germany things are slowly starting to change".
"These papers show how Einstein's creative brain worked, what bothered him and in which order he wrote down his thoughts and conclusions", Gutfreund added. This idea later became the basis for laser technology. In one letter, Einstein praises Besso, a Christian of Jewish descent, for learning Hebrew.
"As a goy [i.e., non-Jew], you're not obligated to study the language of your forefathers, while I, as a "Jewish saint", should be embarrassed by the fact that I know nearly nothing", he wrote.
Roni Grosz, curator of the Albert Einstein Archive at Hebrew University in Jerusalem, called the documents "a rare find". In a letter dated 50 years later, he expresses that he still does not understand the quantum nature of light (I mean, do any of us, really?).
Einstein's more human side can be seen in the personal letters.
"Let's just hope we won't have a Europe war first ... the rest of Europe is now starting to finally take the thing seriously, especially the British", Einstein declared. "If they would have come down hard a year and a half ago, it would have been better and easier", he wrote.
Cortell Reisman's grandmother, Lina Kocherthaler, was Einstein's relative. The Chicago-based foundation purchased the 110-page collection from a private collector in North Carolina for an undisclosed sum.
But some of the papers might require some prior mathematical knowledge to decipher.