Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH3F) by optically pumping the population of 16 M -sublevels in the rotational states J=3, 4, 5, and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M =4 from a few percent to over 70%, thereby generating a translationally cold (≈ 30 mK) and nearly pure state ensemble of about 10 6 molecules. Our scheme is extendable to larger sets of initial states, other final states and a variety of molecule species, thus paving the way for internal-state control of ever larger molecules.Motivated by a multitude of applications ranging from quantum chemistry to many-body physics [1][2][3][4], recent years have witnessed an immense effort to generate cold and ultracold ensembles of polar molecules [5][6][7][8][9][10]. Much of this attention has focused on diatomic molecules, despite unique possibilities for polyatomic molecules [11][12][13][14]. The latter possess additional rotational and vibrational degrees of freedom which could be used for various applications. For example, symmetric-top molecules have been suggested to be ideally suited to simulate quantum magnetism [11,12]. Moreover, precision tests of physics based on chirality require molecules with at least four atoms [13]. In addition, single large molecules have been suggested for the realization of an entire quantum computer, using different vibrational modes to encode individual qubits [14]. Last but not least, the high vapor pressure for many polyatomic molecule species, even at room temperature, allows the efficient generation of high-density initial ensembles [15].A key challenge for obtaining cold and ultracold molecular ensembles has been gaining and maintaining control of the internal molecular state. While this is true for molecules in general, it is particularly problematic for larger, polyatomic molecules. Thus, even for the relatively light molecule CH 3 F discussed here, several thousand rotational states are populated at room temperature. For larger molecules, a huge number of states is populated even at liquid-helium temperatures. Gaining quantum-state control of such molecules requires some form of internal-state cooling. While internal-state cooling has been demonstrated for bialkali dimers [16][17][18] as well as for a number of diatomic molecular ions [19][20][21][22][23], its implementation for polyatomic molecules is lacking.In this Letter, we demonstrate comprehensive internalstate control of the polyatomic molecule methyl fluoride (CH 3 F). In a two-step process, molecules in 16 rotational M -sublevels in the lowest four rotational J states in the |K|=3 manifold are optically pumped into a single rotational M -sublevel (J, K, M being the usual symmetrictop rotational quantum numbers). As a first step, we demonstrate rotational-state cooling (RSC) b...