• I: Introduction.- Mathematics and Modern Physics.- Modern Physics.- Earlier Historical Approaches to Modern Physics.- Mathematics as Language.- Organization of the Text.- I: Eighteenth-Century Science.- II: Vibrating Strings and Eighteenth-Century Mechanics.- III: Eighteenth-Century Physics and Mathematics: A Reassessment.- II: Transitions, 1790–1830.- IV: “Empirical Literalism”: Mathematical Versus Experimental Physics in France, 1790–1830.- V: On the Margins: Experimental Physics and Mathematics in the German States, 1790–1830.- VI: On the Margins: Experimental Philosophy and Mathematics in Britain, 1790–1830.- III: Transformations, 1830–1870.- VII: From Natural Philosophy and “Mixed Mathematics” to Theoretical and Experimental Physics: Britain, 1830–1870.- VIII: Physics and Mathematics in the German States, 1830–1870.- IV: Conclusions and Epilogue.- IX: Physics About 1870 and the “Decline” of French Physics.- X: Epilogue: Forging New Relationships: 1870–1914.

"Garber discusses an interesting part of scientific development, using examples of theoretical physics and their historical steps." ---Mathematical Reviews "Garber argues her case convincingly... A very valuable addition to the existing literature on the history of modern physics. The book is also well written... Those who make an effort to follow the argument will gain many new insights and obtain a fresh outlook at the mathematization of physics in the 18th and 19th centuries." ---Physics World