When the Dutch took Recife, a Jewish community was established soon after, and eventual for the next 14 years, a the community flourished. There were two synagogues as well as all the trappings of a budding Jewish community - Rabbis, schools etc. The Rabbi of Recife was R. Isaac Aboab da Fonseca (his original surname is Aboab, but later in life he took his mother's name Da Fonseca as well) - and Machon Yerushalayim has published some of his writings as well as historic documents relating to the Recife community - Kitvei Rabbenu Yitzhak Aboab (De Fonseca) - Hakhmei Recife v'Amsterdam (Machon Yerushalayim, 2007).
The earliest responsum relating to the Americas concerns the community of Recife. As Recife is in the southern hemisphere and their season are the opposite of those in the northern hemisphere, they asked if they should still say ve'ten tal u'mattar at the time it is normally said as it is not the correct season for them.
R. Aboab, a student of R. Isaac Uzziel, was then appointed to the position of hakham and became the assistant of R. Saul Morteira and eventually took his position as Chief Judge of the Amsterdam court. R. Aboab was successed by R. Yakkov Sassportas.
In 1641 R. Aboab was sent to Recife to become the rabbi and head of the Dutch community there. Although the community was doing well, other forces spelled the demise of the community. In 1646, the Portuguese attacked Recife and although initially they were held off, they eventually were successful in reconquering the city and the rest of Brazil. The Jews were given three months to evacuate or come under the inquisition. R. Aboab, and many others returned to Amsterdam. Other refugees went and established communities in the Caribbean while one group, went to then New Amsterdam (eventually New York) and became the first Jews in New York.
In this new book, there is an extensive introduction, by R. Yosef Veitman, the Chabad shaliach in São Paulo, which gives all the above history and more. R. Veitman has done extensive research and this shows throughout the work. The history is very detailed and the sources consulted -- both traditional and academic -- are quite extensive. The one minor criticism is his use of statements of the prior Lubavitch Rebbi to prove a point of history (see, e.g., p. 39 n. 19 - also see p. 73 n. 123 which, as R. Veitman recognizes is highly suspect), otherwise the research is very good.
Aside from providing a history of R. Aboab and Recife, this work contains Torah from R. Aboab. The most important is the Machberet Nishmat Hayyim. This work was originally in Porteguse, and has now been translated into Hebrew. It has previously been translated into English by Alexander Altmann, "Eternality of Punishment: A Theological Controversy Within the Amsterdam Rabbinate in the Thirties of the Seventeenth Century,' in Publications of the American Academy of Jewish Research 40 (1972): 1-88, which R. Veitman used with permission.  This work dealt with what was a "hot" topic in Amsterdam at the time - whether there is such a thing as eternal damnation. This was very important as many Jews in Amsterdam had relatives in countries under the control of the inquisition and were "practicing" Christians. What would be their status - could their souls ever be redeemed?
R. Saul Morteira essentially said that there is such a thing as eternal damnation. R. Aboab disagreed and penned this work to explain his disagreement. This work has much broader implications for just the inquisition, but to any Jew who for whatever reason did not practice.
Both Nishmat Hayyim as well as R. Morteira's comments are found in this new volume as well as extensive notes. (Also, R. Meneshe Klein, in his approbation has his own take on this issue.)
Aside from this work, the communal laws of Recife are included, as well as a poem R. Aboab wrote on the Portuguese siege of Recife. It is worth mentioning that R. Aboab did not abandon the Recife community when faced with the Portuguese attack, rather he stayed and ministered to the community during this time of need. There are other smaller Torah pieces (including on the Amsterdam eruv) as well as the teshuva discussing ve'ten tal mentioned above.
The work contains excellent footnotes throughout and all in all this is an excellent work, especially for one interested in either the philosophy of reward/punishment or American Jewish history.
I purchased the book from Biegeleisen in Boro Park (718-436-1165), and I assume in Israel, Machon Yerushalayim should have copies.
 Although Altmann published this already in 1974 the "new" Encyclopeadia doesn't update the Cecil Roth entry on R. Aboab and still has that R. Aboab's "work on reward and punishment entitled Nishmat Hayyim [has] not been published." vol. 1 p. 269.