I have the following problem. The file contains many lines already sorted according to their first arguments. Some of these first arguments are repetitive. For each first argument value, I need to keep the first and the last line that contain it. For example,
...
1 234
1 348
...
...
5 483
...
...
7 132
7 154
7 168
7 244
...

will become

...
1 234
1 348
...
...
5 483
...
...
7 132
7 244
...

I am really pulling my hair . Could any expert help me here ?

Assuming your file is sorted as you say - numerically by first field then by second....

input file - jiji.txt

1 234
1 348
3 123
3 124
3 125
5 483
7 132
7 154
7 168
7 244
9 123
10 123
10 124
10 125
10 126
10 194

#!/bin/sh

input_file="jiji.txt"

cut -d' ' -f1 $input_file | uniq |\
  while read val; do
  values=`sed -n "/^${val} / p" $input_file`
  if [ `echo "$values" | wc -l` -eq 1 ]; then
     echo "$values"
  else
     first=`echo "$values" | sed -n '1 p'`
     last=`echo "$values" | sed -n '$ p'`
     echo "$first"
     echo "$last"
  fi
done

exit 0

1 234
1 348
3 123
3 125
5 483
7 132
7 244
9 123
10 123
10 194

Cool !!! Thanks a lot, ZB!!!