  The Levy Walk is the process with continuous sample paths which arises from
consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming
speed 1 and motions in the domain of beta-stable attraction, we prove
functional limit theorems and derive governing pseudo-differential equations
for the law of the walker's position. Both Levy Walk and its limit process are
continuous and ballistic in the case beta in (0,1). In the case beta in (1,2),
the scaling limit of the process is beta-stable and hence discontinuous. This
case exhibits an interesting situation in which scaling exponent 1/beta on the
process level is seemingly unrelated to the scaling exponent 3-beta of the
second moment. For beta = 2, the scaling limit is Brownian motion.
