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An exciting topological foray into Romantic textuality, Fantastic Shapes shows how poetic form participates in a broader reimagining of space and spatial relations at the turn of the nineteenth century. It reveals how the textual surface, far from being a passive carrier wave of content, emerges as an active, shaping force: a dynamic, self-reflexive site of meaning-making. Focusing on four poets - John Keats, Charlotte Smith, Percy Shelley and Felicia Hemans - the book engages with developments in non-Euclidean geometry to argue that far-reaching reconceptualizations of space not only form the backdrop to Romanticism's challenge to classical order, but come to constitute that very challenge. This book's wider aim is to offer fresh perspectives on key Romantic signatures: irony, fragmentation, non-orientability, recursion, and spatial paradox. These formal tendencies, Richard Marggraf-Turley argues, are not merely aesthetic or rhetorical effects but expressions of a deeper epistemic rupture - one that unfolds against a mathematical revolution that was testing, and ultimately disrupting, the constraints of Euclidean spatial logic.