*Contributions to the history of mathematics in Sweden before 1679*was published as a book. We give below a translation of the Introduction. The translation is by Annette Oldsberg, University of St Andrews. We also give some biographical details of two people that Dahlin mentions in the Introduction.

**1. Introduction.**

Decrees and prescriptions issued for the educational system have been used when conducting our research, to the extent that they can be obtained. The later part of the time period that this paper encompasses provided lecture notes, specifying the content that was each year covered in the lectures by the mathematics professors. This resource is necessary for gaining a deeper insight about the state of science in general, as well as its various disciplines, to which, at different points in time, we has chosen to restrict attention to.

In order to provide a clear outline, this thesis is split into two main parts, comprised of the time prior to Uppsala University's revival in 1593, and the period 1593-1679. During the former time period, with the exception of the last 11 years, we were unable to find a Swedish establishment for education in mathematics. As for the latter, there have certainly been mathematics professors lecturing prior to 1620, however, we have not found any written evidence of their work dating back to this time. Only after the last-mentioned year did the academic activities become more lively, as a consequence of the measures taken by the university to reorganise and become a more solid institute. Hence the year 1620 was taken as a divide between two subsections in the latter time space.

During the full time span that our report covers, one did never reach - with trigonometry as the only exception - as far as what today constitutes the minimum level of knowledge that is required to pass secondary school. It is not until after 1679, when both of the old mathematics professors at Uppsala passed away, and the more capable scholars Spole and Bilberg simultaneously took their positions, that we could discover in academic works the use of logarithms, exponents, letter notation in algebra, and a robust notation for analogies.

To not burden our paper with biographical notes, we have generally followed the principle that foreign authors will only be stated if they are mentioned in the works of Montucla, Suter or Poggendorff, that are referenced below. ...

**2. Anders Spole (1630-1699).**

Spole studied at Greifswald University in German, studying subjects such as mathematics, military arts and navigation. During the years 1664-1667 he toured round Europe where he visited leading scientists such as Christiaan Huygens, Robert Hooke, Robert Boyle, Nicolaus Mercator, Ismael Boullieau, Giovanni Cassini and Giovanni Battista Riccioli. He was appointed professor of astronomy at Lund University soon after it was founded in 1666 by Charles XI. He became professor of astronomy at Uppsala University in 1679.The first real astronomer at Uppsala University.

**3. Johannes Bilberg (1646-1717).**