Salamanca is considered to be one of the safest cities in Spain. Violent crime is for the most part unheard of. As with the rest of Spain, you should be aware of pickpockets, but they are less common in Salamanca than in the bigger cities.
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While the streets are filled with international tourists and students from countries around the world most locals do not speak English. It is not uncommon to find even the hotel staff in Salamanca only able to speak Spanish to you. With that said, the locals are used to people butchering their language and are willing be patient with you.
Salamancans Salmantinos in Spanish are very schedule oriented. They wake up, work, eat, shop and sleep at around the same time every day. Almost all stores close at exactly 2PM for a few hours so the staff can lunch. This can be hard for outsiders to adjust to but it's something you have to deal with for however long you are in town.