Once you have completed the basic tones of Mandarin, you will start to notice that they often change. For example, you will hear:
For 你好 (Hello), you will say 【ní hǎo】 instead of 【nǐ + hǎo】；
For 不客气 (You are welcome), you will say 【bú kè qì】instead of 【bù kè qì】
When and where do they change? Actually, there are some specific rules that cause Mandarin tones to change in certain situations. These rules are called the Tone Sandhi.
As a Chinese, I don’t remember when I learned these rules at school, I probably unconsciously acquired it. But having thought about it, I realized they are true, and that I follow it.
Let’s take a look at these rules, and I will add some examples for each of them:
When there are two third tones in a row, the first one changes to a second tone.
  →  
This ‘half third tone’ is a low-pitch tone that falls slightly.
 [1/2/4]→ [half third tone] [1/2/4]
The character 一 (one) is normally first tone (yī), but this changes in two situations.
[一1]  → [一2] 
[一1] [1/2/3] → [一4] [1/2/3]
不 is normally the fourth tone (bù), but there is one situation where this changes:
[不4]  → [不2] 
It is important for beginners to memorize these rules, because sometimes textbooks will not remind you.