Q:

cannot create directory Permission denied - even when using sudo

I am trying to install gsl-2.5 - https://www.gnu.org/software/gsl/. I have used the command sudo ./configure && make && make install, but still run into permission problems:
libtool: link: ranlib .libs/libgsl.a
libtool: link: rm -fr .libs/libgsl.lax .libs/libgsl.lax
libtool: link: ( cd ".libs" && rm -f "libgsl.la" && ln -s "../libgsl.la" "libgsl.la" )
/bin/bash ./libtool  --tag=CC   --mode=link gcc  -g -O2   -o gsl-randist gsl-randist.o libgsl.la cblas/libgslcblas.la -lm 
libtool: link: gcc -g -O2 -o .libs/gsl-randist gsl-randist.o  ./.libs/libgsl.so cblas/.libs/libgslcblas.so -lm
/bin/bash ./libtool  --tag=CC   --mode=link gcc  -g -O2   -o gsl-histogram gsl-histogram.o libgsl.la cblas/libgslcblas.la -lm 
libtool: link: gcc -g -O2 -o .libs/gsl-histogram gsl-histogram.o  ./.libs/libgsl.so cblas/.libs/libgslcblas.so -lm
creating gsl-config
creating gsl.pc
make[2]: Leaving directory '/home/sam/program_files/gsl-2.5'
make[1]: Leaving directory '/home/sam/program_files/gsl-2.5'
Making install in gsl
make[1]: Entering directory '/home/sam/program_files/gsl-2.5/gsl'
make[2]: Entering directory '/home/sam/program_files/gsl-2.5/gsl'
make[2]: Nothing to be done for 'install-exec-am'. 
make[2]: Nothing to be done for 'install-data-am'. 
make[2]: Leaving directory '/home/sam/program_files/gsl-2.5/gsl'
make[1]: Leaving directory '/home/sam/program_files/gsl-2.5/gsl'
Making install in utils
make[1]: Entering directory '/home/sam/program_files/gsl-2.5/utils'
make[2]: Entering directory '/home/sam/program_files/gsl-2.5/utils'
make[2]: Nothing to be done for 'install-exec-am'. 
make[2]: Nothing to be done for 'install-data-am'. 
make[2]: Leaving directory '/home/sam/program_files/gsl-2.5/utils'
make[1]: Leaving directory '/home/sam/program_files/gsl-2.5/utils'
Making install in sys
make[1]: Entering directory '/home/sam/program_files/gsl-2.5/sys'
make[2]: Entering directory '/home/sam/program_files/gsl-2.5/sys'
make[2]: Nothing to be done for 'install-exec-am'. 
 /bin/mkdir -p '/usr/local/include/gsl'
/bin/mkdir: cannot create directory ‘/usr/local/include/gsl’: Permission denied
Makefile:637: recipe for target 'install-pkgincludeHEADERS' failed
make[2]: *** [install-pkgincludeHEADERS] Error 1
make[2]: Leaving directory '/home/sam/program_files/gsl-2.5/sys'
Makefile:918: recipe for target 'install-am' failed
make[1]: *** [install-am] Error 2
make[1]: Leaving directory '/home/sam/program_files/gsl-2.5/sys'
Makefile:963: recipe for target 'install

I am guessing that, for some reason, my root privileges don't include the  /usr/local/include directory.  Does anyone know why this may be the case and how I can fix it? 

A:

Your command
sudo ./configure && make && make install

runs these three commands sequentially:
sudo ./configure
make
make install

Notice that only the first one has root privileges. 
Typically you would run the configure/make stages as your own user account, assigning root privileges only for the final installation stage:
./configure
make
sudo make install

You can join these with && if you're daring.  Personally I prefer to leave the install stage as a separate activity that I apply only when I'm happy that the first two stages have completed not only successfully but also correctly.