What are the section summaries for the book Harvest Of Empire by Juan Gonzalez?

The wording of your question is a bit hard to surmise, but my guess is that you are wanting a summary of the three different sections of the book Harvest of Empire: A History of Latinos in America including the different chapters. In regards to this, the three sections are as follows:  Part 1 (Roots), Part 2 (Branches), and Part 3 (Harvest).

Part 1 is aptly named "Roots" because it is about how all of this began.  The first chapter called "Conquerors and Victims" is about how Hispanics originally formed the American image from the sixteenth to the nineteenth centuries.  It begins with this quote by Castillo:

The arrival of European explorer to American began the most astounding and far-reaching encounter between cultures in the history of civilization.

European explorers, then can be credited with the creation of the Hispanic community in America. The Aztecs, sickness, and the Church are all discussed.  The next chapter is about the "Spanish Borderlands" and the empire made as a result.  Part one ends with a discussion about “Banana Republics and Bonds” and has to do with Hispanic culture up until 1950. 

Part 2 is named "Branches" because it talks about the literal branches that resulted in the offshoots of the Hispanic culture of the Americas.  The chapters are named from each branch:  Puerto Ricans, Mexicans, Cubans, Dominicans, Central Americans, and Columbians.  Each different cultural branch is discussed in turn, with one branch acting more like refugees while another acts more like citizens.  All of the the branches, however, are vowing to combat division and racism.

Part 3 is called "Harvest" and speaks of the time up until the present day.  The issues involved are many and varied.  The chapters reveal this fact.  The chapters range from Latinos in politics, to old and new immigrants, to the speaking of the Spanish language in America, to free trade agreements, and to Puerto Rico being a special case in regards to its title and citizenship.

In conclusion, the author ties it all nicely together by naming the sections in order of the growing of a vast tree:  "Roots," "Branches," and "Harvest."  It brings the image of a "family tree" to mind, and asks readers to connect all Hispanic Americans in that way.  It is a good history of Hispanic culture in America.