certainly used when saying that you are sure about something: 
 Amy’s certainly growing, but she’s not gaining weight.
 Amy’s certainly growing, but she’s not gaining weight.  It’s certainly not the cheapest way of getting to New York.
 It’s certainly not the cheapest way of getting to New York.  ‘Is this his signature?’ ‘Almost certainly.’undoubtedly
 ‘Is this his signature?’ ‘Almost certainly.’undoubtedly used when saying that you are completely sure about something. 
Undoubtedly sounds more certain and a little more formal than 
certainly: 
 They are undoubtedly the better team.
 They are undoubtedly the better team.  Undoubtedly it will be a huge shock for him.
 Undoubtedly it will be a huge shock for him.  The furniture, although undoubtedly fashionable, was a little too plain for my taste.there is no doubt
 The furniture, although undoubtedly fashionable, was a little too plain for my taste.there is no doubt used when you are completely sure about something: 
 There is no doubt that violence on TV influences children.
 There is no doubt that violence on TV influences children.  He’s definitely innocent. There’s no doubt about that.without (a) doubt
 He’s definitely innocent. There’s no doubt about that.without (a) doubt used when you are completely sure about something: 
 She was without doubt one of Mexico’s finest artists.
 She was without doubt one of Mexico’s finest artists.  There would be, without a doubt, some perfectly ordinary explanation for his behaviour.
 There would be, without a doubt, some perfectly ordinary explanation for his behaviour. [TahlilGaran] English Thesaurus ▲