1 Setting the scene.- 2 The humble beginnings.- 3 New prospects in Saint Petersburg.- 4 Formation of an Academician.- 5 Professor of astronomy.- 6 Professional relations and correspondence.- 7 Academic events in Saint Petersburg.- 8 Lexell's work in mathematics.- 9 Academic Journey 1780-1781.- 10 Return to an Academy in crisis.- 12 A sketch of Lexell's personality.- 13 Conclusion.- 14 Appendices.