I trying to make a .hpp file but when I try to compile the compiler is throwing me errors with my constructor.
You should probably read your book.
You don't compile header files (your .h files), change that in your Makefile so its just:g++ Node.cpp LinkedList.cpp -o test
Your .hpp files should be .cpp files for clarity, although it isn't causing any errors.
You're literally doing everything wrong when it comes to defining the template functions.