This is a condensed version of Darksicarius' guide by me (Highlander).

1 - 40
Rough Blasting Powder (1 x Rough Stone)

40 - 50
Handful of Copper Bolt (1 x Copper Bar)

50 - 51
Arclight Spanner (6 x Copper Bar)

51 - 65
Copper Tubes (2 x Copper Bar, 1 x Weak Flux)

65 - 75
Rough Boom Sticks (1 x Copper Tube, 1 x Handful of Copper Bolts, 1 x Wooden Stock)

75 - 95
Coarse Blasting Powder (1 x Coarse Stone)

95 - 105
Silver Contacts (1 x Silver Bar)

105 - 120
Bronze Tubes (2 x Bronze Bar, 1 x Weak Flux)

120 - 125
Small Bronze Bombs (1 x Wool Cloth, 1 x Silver Contact, 4 x Coarse Blasting Powder, 2 x Bronze Bar)

125 - 145
Heavy Blasting Powder (1 x Heavy Stone)

145 - 150
Big Bronze Bombs (2 x Heavy Blasting Powder, 3 x Bronze Bar, 1x Silver Contact)

150 - 175
Blue, Green or Red Fireworks (1 x Heavy Leather, 1 x Heavy Blasting Powder)

175 - 176
Gyromatic Micro-Adjustor (4x Steel Bar)

176 - 190
Solid Blasting Powder (2 x Solid Stone)

190 - 195
Big Iron Bomb (3 x Iron Bar, 3 x Heavy Blasting Powder, 1 x Silver Contact)

195 - 205
Mithril Tubes (3 x Mithril Bar)

205 - 210
Unstable Triggers (1 x Mithril Bar, 1 x Mageweave Cloth, 1 x Solid Blasting Powder)

210 - 225
Hi-Impact Mithril Slugs (1 x Mithril Bar, 1 x Solid Blasting Powder)

225 - 235
Mithril Casings (3 x Mithril Bar)

235 - 245
Hi-Explosive Bomb (2 x Mithril Casings, 1 x Unstable Trigger, 2 x Solid Blasting Powder)

245 - 250
Mithril Gyro-Shot (2 x Mithril Bar, 2 x Solid Blasting Powder)

250 - 260
Dense Blasting Powder (2 x Dense Stone)

260 - 290
Thorium Widget (3 x Thorium Bar, 1 x Runecloth)

290 - 300
Thorium Shells (2 x Thorium Bar, 1 x Dense Blasting Powder)

Approximate Materials Required

90 x Rough Stones
80 x Coarse Stones
75 x Heavy Stones
90 x Solid Stones
50 x Dense Stones
10 x Wooden Stock
29 x Weak Flux
50 x Heavy Leather
10 x Wool Cloth
10 x Mageweave Cloth
33 x Runecloth
51 x Copper Bars
10 x Silver Bars
55 x Bronze Bars
19 x Iron Bars
4 x Steel Bars
126 x Mithril Bars
129 x Thorium Bars
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Engineering 300 to 375 Guide by Highlander on EU-Terenas

300 - 310
Your going to need 55 x Fel Iron Casing, 270 x Handful of Fel Iron Bolts and 35 x Elemental Blasting Powder, so just make all that first and you'll get to 310+.
For every point you go past 310, reduce the the number of items you make by 1 x Fel Iron Casing, 2 X Handful of Fel Iron Bolts and 1 x Elemental Blasting Powder. i.e. the mats required to make Fel Iron Bombs.

310 - 320
Fel Iron Bomb (1 x Fel Iron Casing, 2 x Handful of Fel Iron Bolts, 1 x Elemental Blasting Powder) x 10

320 - 335
Fel Iron Musket (1 x Heavy Stock, 3 x Fel Iron Casing, 4 x Handful of Fel Iron Bolts) x 15

335 - 350
White Smoke Flare (1 x Netherweave Cloth, 1 x Elemental Blasting Powder) x 25

350 - 360
Khorium Power Core (3 x Khorium Bars, 1 x Primal Fire) x 20
It is already yellow when you learn it, but this doesn't turn grey until 370. So after making the 20 you need for the next part, you should be past 360

360 - 375
Field Repair Bot 110G (8 x adamantite Bar, 8 x Handful of Fel Iron Bolts, 1 x Khorium Power Core) x 20

Approximate Required Materials

405 x Fel Iron Bars
9 x Mote of Fire
18 x Mote of Earth
25 x Netherweave Cloth
60 x Khorium Bars
20 x Primal Fire
160 x Adamantite Bars
15 x Heavy Stock