There Will Be Time
by Poul Anderson
Jack Havig was born in the American midwest in 1933 with a genetic mutation that allows him to travel through time. He learns that an apocalypse will occur sometime in the 21st century due to over-pollution and nuclear warfare. Farther still in the future, a New Zealand/Micronesian culture known as "the Maurai Federation" will eventually dominate the world and impose their vision of a less industrialized, more ecologically balanced world. Jack reasons that there must be others born with the same innate ability to travel through time. In his initial search for them, he visits Jerusalem at the time of the Crucifixion. Jack is discovered by other time-travelers who are agents of a time-traveling organization called the "Eyrie," that is based in the far future and is led by a racist man born in 19th century United States. Initially Jack joins the group, but eventually rebels against them when he discovers and experiences first hand the extent of the Eyrie's rampant brutality and inhumanity as they attempt to achieve their goal of stopping the Maurai ascendancy. To defeat the Eyrie, Jack returns to the 20th century and devises a plan of his own to recruit time-travelers and create a "tribe" that will return to the future to destroy the Eyrie.
Much of the story takes place in various times of the past, present, and future, including an extended interlude where Jack is sent on a mission by the Eyrie to medieval Constantinople; where he saves the life of a Greek girl during the carnage of the Fourth Crusade and eventually marries her.
The future depicted in the book is the same as in Anderson's Maurai cycle.