Here we provide a brief and informal introduction to some mathematical and kinematical concepts that are useful in our study of classical mechanics. Vectors in Euclidean space (Appendix A.1) furnish a basic example of a vector spaceVectorspace. The associated notion of linear combinations of vectors with real scalar coefficients leads us to the concept of linear (in)dependenceLinearindependence. The dot or scalar productScalarproduct encodes geometric notions such as lengths, projectionsProjection and anglesAngle while the cross productCrossproduct encodes areas of parallelograms. Together, they allow us to define right-handed orthonormal bases or framesBasisorthonormal. Physically, they are used to define concepts such as the workWork done by a force and the angular momentumAngular momentum of a particle. In Appendix A.2, we use these ideas to introduce the position coordinates and position, infinitesimal displacementDisplacementinfinitesimal, velocityVelocityvector and accelerationAcceleration vectors of a particle moving in Euclidean space. Circular motionCircularmotion (Appendix A.3) and motion with constant acceleration (Appendix A.4) provide examples where explicit formulae for these quantities can be written down. While Cartesian coordinates are the simplest way of specifying the location of a particle in Euclidean space, curvilinear coordinates such as planeCoordinateplane polar and spherical polar coordinatesCoordinatespherical polar (Appendices A.5 and A.6) provide alternatives that are convenient when there is rotational symmetrySymmetryrotation around a central object. By contrast with Cartesian coordinates, new terms arise when we express the velocity and acceleration vectors in polar coordinates since the radial and angular directions change with location, as we will see in Appendix A.5.