Does mass depend on the dimensions in space? Isn't mass the same in which dimension you look? For a one dimensional case, we can write Newton's second law as $F=ma$, but for more than one dimension, it is $F_i=m_ia_i$. Obviously, there can be different velocities and forces in different directions, so they are denoted with an $i$, but why is $m$ also denoted with an $i$?
In other words, is the mass different for different dimensions? There aren't different masses are there? One for $x$-dimension and the other for the $y$-dimension?
Is it just a matter of convention?  
 A: No.  The mass is a scalar quantity, and is therefore the same for each direction.
Not having a copy of the book myself, there are three possibilities that come to mind.  


*

*The first is that Susskind is about to say that it is an experimentally observed fact that $m_x=m_y=m_z$, and so one can simply drop the subscript from the mass and treat it as a scalar.  

*The second is that you are referring to the section on
Newton's 3rd law, in which $\vec F_i = m_i \vec a_i$ refers to the
equation of motion of the $i^{th}$ particle. 

*The third is that it is simply a typo.


If none of these seems to be correct, perhaps a direct quote of the passage in question would shed more light on things.
A: Welcome.
In Special Relativity, mass depends on the speed it has in a certain dimension. If a mass is moving through space (I disregard the time in spacetime) we can put a $(x,y,z)$ inertial frame in space through which the mass moves (in our minds, obviously, but I guess it can be done literally too). 
In every direction the velocity of the mass is different (I'll don't bother you with the math involved). Thus also the relativistic mass, though this is a quite old notion. 
Nowadays the energy (instead of mass) is a better approach. The time component which I left out is part of $(ct,-x,-y,-z)$ of the Minkowsky spacetime.
I hope you understand what I wrote. I'm not sure how far you are with your study (if you study). 
