This proposal aims to study the dust formation processes in the wind of low- and high-mass, evolved stars to gain knowledge on the way cosmic dust is formed and processed in our local and far universe. The proposal focuses on understanding how oxygen-rich and carbon dust is produced in these environments. The nucleation stage of dust formation is described using a novel approach based on chemical kinetic and the inclusion of dust nanoclusters. Nucleation is coupled to the dust condensation phase described by various formalisms. For carbon dust, the aims are twofold: (1) description of carbon dust formation including the synthesis of polycyclic aromatic hydrocarbons (PAHs) and grapheme in hydrogen-rich environments such as carbon stars; (2) model of the carbon dust production routes that include fullerene and carbon cages in hydrogen-poor and hot environments such as Wolf- Rayet massive binaries. The oxygen-rich dust study will focus on the formation of metal oxides (e.g., alumina Al2O3 and spinel Mg2Al2O4), silica and silicate dust in O-rich, evolved stellar environments such as Mira stars and supergiants. The broad objectives are: (1) characterize the dust chemical composition and derive dust mass yields in these objects; (2) study the wind acceleration mechanism in the dust formation zone of Mira and supergiant stars; (3) identify a population of nanoclusters that survive the nucleation and condensation of dust and may be responsible for still unidentified bands observed in these stars; and (4) assess the contribution of AGB stars and massive stars like supergiants and Wolf-Rayet stars to the dust budget of the local and far universe. These research lines are entirely new, novel, and timely as observational data of AGB and supergiant stars from the Herschel telescope are continuously released, and these stellar objects are ALMA key targets. The proposal will thus provide the astronomical community with new, crucial, and topical predictions on dust, molecules, and large clusters in these evolved stellar objects, and assess their impact on the dust budget of local and primeval galaxies. To achieve the objectives of this ambitious programme, we ask for 2 PhD student positions, equivalent to a total budget amounting to 334’800 CHF for the 3-year length of the project. The proposal is connected to the current study of dust synthesis in O-rich Mira stars (SNF project 200021_132616). The first year of one of the requested PhD positions corresponds to the 4rth year PhD extension for David Gobrecht, currently employed under the project 200021_132616.