Understanding operator precedence in Tourlakis's Mathematical Logic

Question

In Mathematical Logic by George Tourlakis p. 15, priority of operators is explained in this terms:

So, two questions:

• What's the meaning of an operator "gluing first" ?
• What's the meaning of "all connectives are right associative" ?

Answer 1

What's the meaning of an operator "gluing first" ?

$P\circ Q * R$

$\circ$ gluing first

$$(P\circ Q) * R$$

$*$ gluing first

$$P\circ (Q * R)$$

What's the meaning of "all connectives are right associative" ?

associative (meaning the operations can be grouped arbitrarily):
$$P\circ (Q \circ R)=(P\circ Q) \circ R$$ left-associative (meaning the operations are grouped from the left)
$$(P\circ Q) \circ R$$ right-associative (meaning the operations are grouped from the right)
$$P\circ (Q \circ R)$$ non-associative (meaning operations cannot be chained, often because the output type is incompatible with the input types) $$P\circ (Q \circ R)\neq(P\circ Q) \circ R$$

See also Operator associativity