What are the logical and arithmetical functions from the 74LS181

Question

i want to use the 74ls181 in an Project of mine but i can not understand all of the functions of it mentioned in its datasheet. Could someone please explain this boolean-mess?

EDIT:

Based on the very helpful answer from Axel Kemper i created this:

Answer 1

Your table was taken from the Texas Instruments 74ls181 datasheet?

Assuming from your question tags that you are asking about the logical functions
(explained from top to bottom as in the table):

F = NOT(A)            set output to inverse of all A bits
F = NAND(A, B)        inverse AND of inputs
F = OR(NOT(A), B)
F = 1                 set all output bits to 1
F = NOR(A, B)
F = NOT(B)            feed inverse B bits to output
F = NOT(EXOR(A, B))
F = OR(A, NOT(B))
F = AND(NOT(A), B)
F = EXOR(A, B)        output is exclusive or of inputs
F = B                 feed B inputs bits to outputs
F = OR(A, B)          bitwise disjunction
F = 0                 set all output bits to 0
F = AND(A, NOT(B))
F = AND(A, B)         bitwise conjuction 
F = A

All functions are implemented 4-bit parallel. A, B and F each have four signal lines. A and B are the four-bit inputs. F is the four-bit output.

So, A=0 for example means A0=0, A1=0, A2=0, A3=0

There is a total of 16 different logical functions possible to implement with two inputs and one output. 74ls181 implements all of them.

A truth-table with two inputs and one output has four rows. Each of the rows has output value 0 or 1. Therefore, a four-bit number defines the function described by the truth-table. With four bits, 16 functions are possible.

There is a very instructive YouTube video available on the 74ls181.