In this work we construct an eigencurve for $p$-adic modular forms attached to an indefinite quaternion algebra over $\mathbb{Q}$. Our theory includes the definition, both as rules on test objects and sections of a line bundle, of $p$-adic modular forms, convergent and overconvergent, of any $p$-adic weight. We prove that our modular forms can be put in analytic families over the weight space and we introduce the Hecke operators $\mathrm{U}$ and $\mathrm{T}_l$, that can also be put in families. We show that the $\mathrm{U}$-operator acts compactly on the space of overconvergent modular forms. We finally construct the eigencurve, a rigid analytic variety whose points correspond to systems of overconvergent eigenforms of finite slope with respect to the $\mathrm{U}$-operator.