Get strings from Serial.read() I want to read strings from Serial.read() to send them later.

To get the data from the Serial monitor I'm doing this:

String stringOne  = "";
int  incomingByte; 

if (Serial.available() &gt; 0) {   

  while(Serial.available() &gt; 0)
  {
     incomingByte= Serial.read();
     stringOne = String(stringOne + String(incomingByte));
  }

  Serial.println(stringOne);
  stringOne = "";


The issue is that when I type:

'a'


I got:

'97'


for 
    'abc' 

I got

'979899'


so on and so forth.

What should I do in order to get the same string I type?
You're adding the ASCII value of each char to your string, hence you get numbers. See the various String constructors at:
https://www.arduino.cc/en/Tutorial/StringConstructors

Either cast the read byte to a char:

stringOne = String(stringOne + String((char)incomingByte));


or consider receiving characters as chars, instead of ints:

char incomingByte; 


There is a perfectly valid one-method call which does all of this hassle easier and more efficiently: https://www.arduino.cc/en/Serial/ReadStringUntil

Note that you'll sooner or later anyhow have to add a framing prototcol. For example, you're sending down text commands to Arduino, and each command is separated by a new line character. ReadStringUntil will handle that very nicely.