You will need to apply at the embassy or consulate of the country where you plan to spend most of your visit, or, if spending an equal amount of time in two countries, the one which you will visit first. However, for many countries, you will not apply to the embassy but via a outsourced visa application center which acts on its behalf for the initial stages of visa processing, such as checking supporting documents and collection of any fees. For example, the firm VFS Global handles visa applications on behalf of Italy and many other countries, while France is represented by the firm TLScontact.
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