I. The optics of the telescope as known when its manufacture was commenced in England.Lipperhey's influence on the Continent and in England; A. M. v. Schyrle's great invention of the terrestrial telescope with image-erecting lenses in 1645 (made in Augsburg).II. The old refracting telescopes in England.Sir Charles Cavendish's acquaintance with A. M. v. Schyrle and some points of similarity between Cock's terrestrial telescope of 1673 and A. M. v. Schyrle's description of 1645. Popularity of telescopes of Schyrle's planning in England in the seventeenth and eighteenth centuries. English improvements and night telescopes.III. The reflecting telescopes after Gregory and Newton, and their manufacture in London.The original work of Gregory and of Newton; J. Hadley's impulse; influence on English opticians; Passement's form in 1738; Short's splendid instruments. Caleb Smith's improvement in 1740 and the first publication of his principle of colour correction.IV. Chester Moor Hall's invention of the achromatic telescope (1729-33) and its marketing by John Dollond (1758).Relation of the already known facts in historical sequence; invention certainly known to the trade in 1754. J. Dollond's re-invention and publication. Prices of such instruments before and after J. Dollond's death in 1761 and Lord Camden's decision in 1766. P. Dollond's policy as to the prices for achromatic telescopes.IV a. A digression concerning the gradual appreciation of Chester Moor Hall's merits.The publications of A. M. de Rochon and Montucla and the work of the more modern investigators A. C. Ranyard, R. B. Prosser, and E. Wyndham Hulme.V. Sir William Herschel's reflectors.Knowledge enlarged by Prince Troubetzkoj and W. H. Steavenson. Herschel's influence on English and foreign opticians beyond the period treated here.VI. The earlier endeavours to avoid a secondary spectrum.A. C. Clairaut in 1762, R. J. Boscovich about 1767 and R. Blair after 1787, employing different fluids.VII. Later improvements and modifications of the achromatic telescope.P. Dollond; H. Pyefinch; brass draw-tubes about 1783; stands folding into a very small compass; W. Worris; C. Varley; the problem of optical glass. The first knowledge of Fraunhofer's instruments; French astronomical objectives of large diameter; the order to Fraunhofer in Munich from Edinburgh Observatory.