What does $f(x\mid\theta)$ denote?
Isn't it interprets that- "here $\theta$ is known then what is the distribution of X for the known $\theta$?"
Then why in the book which i am reading wrote that -- "the function $f(.\mid\theta)$ is assumed known except for $\theta$?"
If $\theta$ is known then why will the function be unknown for $\theta$?
Again, if the statement of the book is true [i know, it is true but I am not understanding] then how is $f(.|\theta)$ known at every point except for $\theta$?
Again, why the is book using the notation $f(.|\theta)$ instead of $f(x|\theta)$ ? Why is the dot(.) being used instead of $x$? that is what does $f(.|\theta)$ symbolize?
A dot represents what's called a placeholder variable. It's a space where I can put a number. $x$ represents an actual number.
So the ordinary density $f(x)$ is the value of the density at $x$. We might not know $x$ but technically it still has a value. Which means $f(x)$ is a number.
But the density itself is a function that is take a number (perhaps $x$) and follow a set of instructions to get another number.
$f(\cdot)$ represents the set of instructions itself, not the result of those instructions when carried out at $x$. That's why we've left a little dot, to tell you where to put an $x$.
For example I can define a function on two variables by setting $$g(x,y) = \frac xy$$
That's a statement that's true for every pair $x,y$ ($y\neq 0$). It's not the function itself, it's just something I'm writing to help you know what I mean by the function $g = g(\cdot,\cdot)$.
Of course that function already had a name it's usually denoted by $$g=\, \frac{\,\cdot\,}\cdot$$
So for the conditional density $f(\cdot|\theta)$ is a function of one variable, if you give it a value $x$ it gives you a value $f(x|\theta)$.
The reason the book uses a dot here is because if it just wrote $f$ it could be referring to the function $f(\cdot|\cdot)$ on two variables, or even the function $f(x,\cdot)$ which takes $\theta\mapsto f(x,\theta)$.