I don't really understand, why the inward current (for example, during depolarization the flow of Na+ inside the cell) is negative? In the textbooks, it is always depicted with minus values (see picture). Ion current is supposed to be positive in the direction of positive charge movement, Na+ is positive, then why is the inward current negative? Thanks in advance.
This is just a chosen convention in biology. All that matters is we use a consistent convention. The one chosen is that outward positively charged ion movement is positive, inward positively charged current is negative; outward negatively charged current is negative, inward negatively charged current is positive.
It would be valid to do everything the opposite way, just change some signs in relevant equations, but since this is the convention everyone uses it's best to stay consistent with it.
Importantly, there is not really a conflict with "current direction is the way positive charge would flow" convention in physics, it's just that you have to determine a reference point. We think of the inside of a cell as the reference, so when positive charge moves from the reference to outside the reference (outward current), we call this positive current. We plot positive currents moving in the opposite direction as negative, which makes sense, but rather than only calling these "negative current" we recognize that this means positive charge is moving inward so a synonym is "inward current".
This convention is also consistent with the convention chosen for voltage. We describe a "negative membrane potential" when the inside is negative relative to the outside. Current is given by:
I = V/R
So, when membrane voltage is negative we say the inside is more negative than outside, and we get a "negative current" if we open some sodium channels and let those positive ions move in. If we used the other current convention we'd have to use a non-standard equation like
I = -V/R
or change the direction in which we describe voltage across the membrane to describe the potential of the outside rather than potential of the inside.