**List of typos:**

P9, L2: \kappa(x) should be \kappa(z).

P32, L4: \phi_d in the second formula should be \phi_d(1,j)=( (3/4)^j , 1/4 (3/4)^{j-1} )

P34, L-8: It is not the case that \phi_b jumps out of the union of the jump set and the closure of the flow set.

P37, L38: Equation t_{i_1+1}-t_{i_1}\geq \tau_D should be t_{i_k+1}-t_{i_k}\geq \tau_D.

P37, 11 lines below (2.5): "If \sigma in a solution" should be "If \sigma is a solution"

P38 Figure 2.8(a): caption should be “\tau_D smaller than or equal to...”

P38 L-3: f_q(\phi) should be f_q(z).

P39, L8: Since we are characterizing a solution to (2.5) which involves sigma and not q, it should say \sigma'(t)=q(t,j).

P53, L-8: the correct definition should be delta = alpha_2^{-1}( alpha_1 (epsilon) ), R = alpha_1^{-1} (alpha_2(r) ).

P54, L5: The subscript "{\cal A}" should be after the right vertical bar.

P60: the brackets are missing for the equation number in 'in place of bound 3.5'.

P62, L3 from beginning of proof: the sign of the exponent of e should be positive.

P101, first line of Definition 5.8: remove "Domain".

P102, sixth line of Definition 5.9: it should be "from R^m to R^n" instead of "from R^n to R^m".

P104, Example 5.13: the value of T_{S}(x) for x = a should be [0,\infty) and the value for x = b should be (-\infty,0].

P122: instead of "semicontinous mapping" it should be "semicontinuous mapping"

P129, 7th line of Example 6.20, it is not true that S_1 is weakly backward invariant and weakly invariant. The text right below S_1 should read "is weakly forward invariant (the forward invariance property is in fact "strong" as it holds for every solution to $\cal H$). The set $S_1$is not weakly backward invariant since points in the interior of the third and fourth quadrants cannot be reached for arbitrary large $\tau$."

P131, 4th line of proof of Prop. 6.26, "forward" should be "backward".

P136, the title of Proposition 6.35 (page 136) should be "non-Zenoness and non-continuousness".

P148: In Example 7.16, it should read:

"For the latter statement, note that for any function $\rho : \mathbb{R} \rightarrow \mathbb{R}_{\ge 0}$ with $\rho(1) > 0,$ …"

P148, in Lemma 7.17, it should A \subset U rather than A \subset BpA.

**List of clarifications:**

In Appendix: List of Symbols: Given sets A and B, the symbol \subset in "A \subset B" indicates that A is a subset of B, not necessarily a proper subset.