Are branes as fundamental as strings or not? Are D-branes in string theory as fundamental as one-dimensional strings, or are strings more fundamental and multi-dimensional branes are "woven" from one-dimensional strings?
 A: 
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions

They are called generically string theories, but if a theory is based on branes, the concept of  one dimensional string  representing elementary point particles has developed into two dimensional branes representing elementary particles.
A: $D$-branes are as "fundamental" as fundamental strings, at least in the two following precise ways:

*

*String dualities (the symmetries of string theory as a whole) exchange fundamental strings with D-branes. As an example, the $SL(2,\mathbb{Z})$ symmetry of type $IIB$ string theory mix fundamental strings and 1-branes (see An $SL(2,\mathbb{Z})$ Multiplet of Type IIB Superstrings ).

*Fundamental strings descend from $M$-branes in the similar ways as $D$-branes descend from $M$-branes. The prototypical examples are type $IIA$ fundamental strings at finite coupling as $M2$-branes wrapped in the eleven dimension of $M$-theory, and $D2$-branes as unwrapped $M2$-branes. They are the same object, just with different geometry (which obviously has important dynamical imprints). See the beautiful $P$-brane democracy and P-branes from M-branes for further details.

