Why multiply first? Why do we multiply/divide first, and then add/subtract later?
I mean, what I'm curious about is that is this a universal rule, or a man-decided rule? Also how would you decide on which to operate first?
For example, if we were to be visited by aliens, would they be using the same math? Would they also multiply first, add later?
 A: This is just a notational convention to allow one of the expressions $$(a+b)\cdot c\qquad a+(b\cdot c) $$be written without parentheses. One could have chosen the other (or to always require parentheses), but think how complicated it would make writing e.g. polynomials (unless written as product of linear factors).
The same considereation holds for why $a-b-c$ stands for $(a-b)-c$ and not for $a-(b-c)$. Alternatively, one might introdue a prefix ore postfix (instead of infix) notation, aka. (reverse) Polish notation, i.e. $ab+c\cdot$ or $\cdot +abc$ vs. $abc\cdot+$ or $+a\cdot bc$.
A: Complementary to what others said, the order of operations is also a natural consequence of rewriting expressions to avoid ambiguity. 
For example, $3\times 4+1$. If this were all addition, there’d be no problem, because addition is commutative and associative. To rewrite this with only addition: $4+4+4+1$, so you’re essentially evaluating the multiplication first to make it unambiguous. Same is true for exponents and other hyperoperations like tetration. And without choosing a set order multiplication and addition would lose associativity and commutativity, eg sometimes $3\times 4+1\neq 4\times 3+1$ (which would surely lead to problems in defining other functions elsewhere). It’s completely a choice, but does make things clearer and simpler, and as others have pointed out tends to be more useful. 
A: The order of operations were "man-made". If there were no such thing as "Order of Operations", an expression like $3+4\times 7+2^2\div 4$ can have many different answers. One could add $3+4=7$, then times $7$ to get $49$, then plus $2^2$ to get $53$, and finally divide by $4$ to get $\dfrac{53}{4}$. But if we follow the order of operations, we would get a different answer.
$$3+4\times 7+2^2\div 4=3+4\times 7+1=3+28+1=32$$
To avoid these different answers, we created the Order of Operations so that each expression has only one answer.
