global-analysis-and-the-banach-manifold-of-class-h1-curvers

diff --git a/sections/applications.tex b/sections/applications.tex
@@ -510,7 +510,7 @@ however, is the following consequence of Morse's theorem.
   as \(X \to 0\).
 
   Let \(\gamma\) be as in \textbf{(i)}. Since \(\gamma\) has no conjugate
-  points, it follows from Morses's index theorem that \(T_\gamma^- \Omega_{p q}
+  points, it follows from Morse's index theorem that \(T_\gamma^- \Omega_{p q}
   M = 0\). Furthermore, by noticing that any piece-wise smooth \(X \in \ker
   A_\gamma\) is Jacobi field vanishing at \(p\) and \(q\) one can also show
   \(T_\gamma^0 \Omega_{p q} M = 0\). Hence \(T_\gamma \Omega_{p q} M =
@@ -553,7 +553,7 @@ classical formulation: we can find curves \(\eta = i(v)\) shorter than
 
 This concludes our discussion of the applications of our theory to the
 geodesics problem. We hope that this short notes could provide the reader with
-a glimpse of the rich theory of the calculus of variations and global anylisis
+a glimpse of the rich theory of the calculus of variations and global analysis
 at large. We once again refer the reader to \cite[ch.~2]{klingenberg},
 \cite[ch.~11]{palais} and \cite[sec.~6]{eells} for further insight on modern
 variational methods.

diff --git a/sections/introduction.tex b/sections/introduction.tex
@@ -75,7 +75,7 @@ discuss neither technicalities nor more involved applications of the theory we
 will develop.
 
 In particular, we leave the intricacies of Palais' discussion of condition (C)
--- wich can be seen as a substitute for the failure of a proper Hilbert space
+-- which can be seen as a substitute for the failure of a proper Hilbert space
 to be locally compact \cite[ch.~2]{klingenberg} -- and its applications to the
 study of closed geodesics out of this notes. As previously stated, many results
 are left unproved, but we will include references to other materials containing