sauces that are suggested for culinary school people to learn that aren't European

Sauces I've seen recommended as "must-learn" for cooks:

• Chimichurri, from Argentina and Uruguay
• Jeow Som
• chutney, from India
• salsa
• peanut sauce, from Indonesia

And yes, some European sauces are important too

• list of French sauces [2]
• list of Italian pasta sauces

Specific sauces:

• barbecue sauce, from America
• Bolognese sauce, an Italian meat-based sauce (specific instructions for cooking in a wok)
• tzatziki sauce, from Greece
• Romesco sauce, from Spain
• aioli, from Spain and France

Sources

[1] [2] [3] [4]