Lawrence provides a lot of background information that really sets the stage for why the Middle East is such a tense place. Also a lot of in depth personal history of not only the main characters but also many of the supporting cast.
The three men, Jimmy Carter, Menachem Begin and Anwar Sadat had conflicting personalities and viewpoints with one shared trait. They all had religious beliefs, but they were in some ways counter productive. Menachem Begin felt that the Jews deserved more land than they were originally given. Jimmy Carter, a Sunday school teacher, then as now felt settlements on occupied lands were a provocation. Anwar Sadat felt Egypt should represent the Arab and Muslim grievances.
Jimmy Carter wanted to be a facilitator letting the other two work out differences, but that failed. Originally thought the process required 3 or 4 days, but dragged on. Jimmy and his American team (Zbigniew Brzezinski and Cyrus Vance were key) then made proposals and looked for some sign of bending which occurred only after a lot of stress.
Tempers flare as there is a lot of obstinacy. Each leader had his flaws--in the end political realities played a role. Once they had invested some effort they each needed something to show for the effort. Egypt wanted land, Israel wanted better relations--Jimmy Carter needed something to make him look good.
A few oddities included that Sadat was descended from a slave and had negro blood. Boutros Boutros-Ghalli who later became prominent at the Untied Nations was a Coptic Christian, and married a Jew. Zbigniew Brzezinski and Menachim Begin both shared a Polish heritage and enjoyed playing each other in chess.
In the end diplomatic relations were established between Israel and Egypt that also facilitated trade benefits. The Sinai Peninsula was returned to Egypt including oil resources. The Suez Canal is accessible to everyone. A surprising detail is that since 1979 there has not been a single violation of the terms.
The Palestinians were abandoned as their inclusion would have negated the rest of the treaty that could be worked out. Originally they were an important component, but Begin would not budge and both Egypt and United States desperately wanted something to be agreed upon.
There was quite a political risk for Jimmy and in the end it wasn't enough. The Iran crisis and a stagnant economy did him in. Nobody since has made as much progress and the agreements were not enough of a building block to stop violence. Jimmy Carter has said (and I agree) that the biggest obstacle is Jewish settlements on occupied land. That is such an emotional issue on both sides that nothing will go forward until it is resolved.
Another step towards peace was taken under Bill Clinton, another Democrat president when he facilitated an agreement between Jordan and Israel in 1994. Still no real impact on the Palestinians.