diff --git a/doc/usecases.tex b/doc/usecases.tex
index b3a9337..55209e1 100644
--- a/doc/usecases.tex
+++ b/doc/usecases.tex
@@ -45,11 +45,11 @@ \subsubsection{Euclid}
 about the shapes of galaxies, gravitational lensing, baryon acoustic oscillations,
 and distances to galaxies using spectroscopic data.
 
-For this mission, and apart from the common metadata provided for extra galactic
+For this mission, and apart from the common metadata provided for extragalactic
 sources into astronomical catalogues, a good support for object taxonomy and
 shapes of objects is required. As known due to general relativity effects,
 shapes of far galaxies could be deformed due to gravitational lensing effects,
-producing convergence (visual displacements on the position) and rear (deformation
+producing convergence (visual displacements on the position) and shear (deformation
 of the shape) effects. All these metadata should be ready for annotations and,
 also, correlated to theoretical or real metadata in other datasets.
 
@@ -75,7 +75,7 @@ \subsubsection{Exoplanets}
 Annotation of exoplanetary records in catalogues requires some
 specific metadata or model.
 
-The use cases identified requires the following metadata:
+The use cases identified require the following metadata:
 \begin{itemize}[noitemsep,topsep=0pt,parsep=0pt,partopsep=0pt]
 	\item the degree of confidence in the detection: exoplanets candidates
           with respect to confirmed ones, plus last update of the record content;
@@ -132,7 +132,7 @@ \subsubsection{X-ray Observatory Archives}
                \item complex errors (asymmetric, ellipse);
                \item model-based data (flux, spectra).
            \end{itemize}
-    \item X-ray data are often analyzed in conjunction with data from other domains, 
+    \item X-ray data are often analyzed in conjunction with data from other domains. 
           This is made easier if they all have the same way of describing the quantities of interest.
 \end{itemize}