This is a new edition of the volume first published in 1891. Translated for the Hakluyt Society, and with notes and an introduction, by Luis L. Dominguez, this volume presents the accounts of the first two historians who wrote on the conquest of the Rio de la Plata, which took place in the reign of Charles V, King of Spain and Emperor of Germany. The first of these was a German, a native of Straubing, in Bavaria, whose name was Ulrich Schmidt. Schmidt published a narrative of his voyage under the title "Warhafftige und liebliche Beschreibung etclieher fürnemen Indianischen Landschafften und Insulen, die vormals in keiner Chronicken gedacht, und erstlich in der schiffart Ulrici Schmidts von Straubingen, mit grosser gefahr erkündigt, und von ihm selber auffs fleissigst beschrieben und dargethan." The first part of this volume is the book translated into English, for the first time, from the original German, and now published by the Hakluyt Society. The second was a Spaniard, native of Jerez de la Frontera in Andalusia, named Alvar Nuñez, better known by the surname which he took from his mother, Doña Teresa Cabeza de Vaca. Nuñez published a narrative of the events that had happened to him during his term of office, viz., from 1541 to 1544. This record, the first published on the conquest of the Rio de la Plata and Paraguai, appeared in Valladolid in 1555, under the general title "Relacion y Comentarios de Alcar Nuñez Cabeza de Vaca, de lo acaecido en las dos jornadas que hizo à las Indias. The Relacion refers to his adventures in Florida, and was first published in 1542,1 while the Comentarios appeared as a second part of the new edition of his voyages under the title just mentioned. This is the second book contained in the present volume.