Some definitions:
Vertex a point in 3D space.
Edge a line in 3D space that has 2 vertices (plural of vertex) on its two ends
Face is a triangle area defined by 3 edges (quads using 3 edges are not commonly used). In the result, faces are visible and edges and vertices are invisible.
Mesh is your 3D objects edges and vertices.
There are different projections:
Orthographic projection is the projection used in technical drawings. All angles stay the same. It is the favor projection for modeling. However the size of an object stays the same when it gets moved in the distance, therefore it does not give realistic views.
Isometric projection
Perspective projection, makes things that are in far distance to appear small. If put very far that every object becomes just a point. There are also two and three point perspective projections.
Coordinate systems need some definitions. The right hand method assigns positive directions of the x,y,z axis to where the fingers (thumb, index, middle finger) of the right hand point (when having 90 degrees between them).
Additionally there are also rotations. Positive rotation is (according right hand rule) when the thumb points in the positive direction to the axis and then the other fingers point in to the rotating direction.
3D objects can put together, so a hierarchical structure is formed between them. Every object has its own coordinate system in the global coordinate system.
3D modeling sw for linux are: openscad, blender, wings3D, k-3d http://www.k-3d.org/, aoi http://aoi.sourceforge.net/index
Models are available fromhttps://www.thingiverse.com/ https://www.tinkercad.com/things/ https://grabcad.com/library/software/stl http://sketchup.google.com/3dwarehouse
A very big issue is that the 3D objects have to be manifold, especially when it comes to 3D printing. A good explanation of manifold is that the objects are watertight. Using faces, just the surface is described, therefore objects are like plastic bags, when they are manifold (watertight) and filled with water, no water runs out. Unfortunately many 3D design software can create complicated meshes that are not manifold.
A good software is openscad, since it does not work with meshes, it works with Constructive Solid Geometry (CSG) and when the work is done, it can be converted in a mesh that is usually as simple as possible and manifold.
A bad example in this point of view is blender. When applying the boolean modifier to punch a lot of holes in an object a terrible complicated mesh is created. When then moving the holes around a non manifold very complicated mesh gets created. To fixing that manually hours of work is required.
Meshlab http://www.meshlab.net is a tool to clean up a mesh